1. Home Page J. S. Milne. Mathematics site of J.S. Milne; course notes preprints, and other manuscripts. Fields and Galois Theory. algebraic geometry. Algebraic Number Theory October 30, 2003 Revised version of algebraic geometry. August 31, 2003 Corrected version of Fields and Galois http://www.jmilne.org/math

2. AG Algebraic Geometry Papers and preprints. http://front.math.ucdavis.edu/math.AG

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ AG Algebraic Geometry Conferences Calendar Search Authors: All AB CDE FGH ... U-Z New articles (last 12) 4 Jun math.AG/0406066 Equivariant Quantum Schubert Calculus. Leonardo C. Mihalcea . 24 pages. AG CO 3 Jun math.AG/0406030 Vector bundles and theta functions on curves of genus 2 and 3. Arnaud Beauville . 12 pages. AG 3 Jun math.AG/0406026 Topological invariants of O'Grady's six dimensional irreducible symplectic variety. Antonio Rapagnetta . 30 pages. AG 2 Jun math.AG/0406016 Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces. Eyal Markman . 53 pages. AG Cross-listings 3 Jun math.RT/0406034 Iterated extensions in module categories. Eivind Eriksen . 24 pages. RT AG RA 3 Jun math.CV/0406023 A criterion for the logarithmic differential operators to be generated by vector fields. Mathias Schulze . 11 pages. CV AG Revisions 4 Jun math.AG/0312059 Gromov-Witten theory and Donaldson-Thomas theory. D. Maulik , N. Nekrasov , A. Okounkov , R. Pandharipande . 31 pages. ITEP-TH-61/03, IHES/M/03/67. AG 4 Jun math.AG/0307209

3. Journal Of Algebraic Geometry Online The Journal of algebraic geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory http://www.ams.org/distribution/jag/

Journals Home Search Author Info Subscribe ... All issues Authors Author Packages Initial Submissions Where to send files for accepted papers Manuscript tracking About Editorial Board The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles posted individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website. Subscriptions: Subscriptions to this journal can be obtained through the AMS Bookstore . Subscriptions and orders can also be addressed to the American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904. All orders must be accompanied by payment. A License Agreement is available electronically.

4. Algebraic Geometry algebraic geometry. algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with http://www.math.byu.edu/People/links/jarvis/alg-geom.html

Algebraic Geometry Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate. David Mumford Sources for preprints and other texts Preprints at arXiv.org The canonical place to get and post the latest research in math. EMANI Electronic Mathematical Archiving Network Initiative Excellent free electronic source. Grothendieck-Circle.org the most complete source for material by and about Alexandre Grothendieck. JSTOR The scholarly journal archive (large collection of important sources, but limited access without subscription) Other General Sites European Algebraic Geometry: AGE and EUROPROJ Tata Institute of Fundamental Research IAS/Park City Summer Mathematics Institute Algebraic Curves Projections of complex plane curves to real three-space A Visual Dictionary of Special Plane Curves Overview of Algebraic Plane Curves (Geometry Center) Famous Curves Index (University of St. Andrews) Algebraic Surfaces , or Surfaces with many ordinary nodes.

5. 14: Algebraic Geometry 14 algebraic geometry. Introduction. algebraic geometry combines the algebraic with the geometric The historical development of algebraic geometry", Amer. Math. Monthly 79 (1972 http://www.math.niu.edu/~rusin/known-math/index/14-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 14: Algebraic geometry Introduction Algebraic geometry combines the algebraic with the geometric for the benefit of both. Thus the recent proof of "Fermat's Last Theorem" ostensibly a statement in number theory was proved with geometric tools. Conversely, the geometry of sets defined by equations is studied using quite sophisticated algebraic machinery. This is an enticing area but the important topics are quite deep. This area includes elliptic curves. History Applications and related fields geometry (in particular for conics and curves), algebra (since algebraic geometry is commutative ring theory...) number theory (especially for Diophantine analysis). Subfields Foundations Local theory, see also 32SXX Cycles and subschemes Families, fibrations Birational geometry [Mappings and correspondences] (Co)homology theory, see also 13DXX Arithmetic problems. Diophantine geometry, see also 11DXX, 11GXX 14H: Curves 14J: Surfaces and higher-dimensional varieties . For analytic theory, see 32JXX

6. Books By Jean-Pierre Demailly Book by JeanPierre Demailly in PostScript. http://www-fourier.ujf-grenoble.fr/~demailly/books.html

Books by Jean-Pierre Demailly (last update: November 10, 2000) Complex analytic and algebraic geometry I just got cancelled a stupid agreement I signed long ago with a publisher. This means that my book will soon be available as an "OpenContent Book", i.e. that you can get the source file for free and do whatever you like with it on the web (print it, spread it, modify it, etc...) except claiming that you are the author! At the moment, it is still not completely achieved and the TeX file is not polished enough. Instead, here is a (compressed) PostScript file of the current version: agbook.ps.gz

7. Algebraic Geometry algebraic geometry. What is algebraic geometry? algebraic geometry is a subject with historical roots in analytic geometry. At its most naive level it is concerned with the geometry of the solutions http://www.math.tamu.edu/~Peter.Stiller/agpage.html

Algebraic Geometry What is Algebraic Geometry? Research Interests: For a list of related publications, click here Return to TAMU Math Return to Dr. Stiller's home page

8. Algebraic Number Theory Archives Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. 18, 2000, Bounding minimum distances of cyclic codes using algebraic geometry, by http://www.math.uiuc.edu/Algebraic-Number-Theory

Algebraic Number Theory Archives Date: Wed, 8 Jan 2003 12:03:33 -0600 (CST) To: Algebraic-Number-Theory@listserv.uiuc.edu Subject: Algebraic-Number-Theory preprint archives I shall no longer be managing the Algebraic Number Theory preprint archives. The web site is now frozen and is not accepting new submissions and subscriptions. Michael Zieve has kindly agreed to assume control, with the help of Greg Kuperberg, and new submissions should be directed to the new URL for the archive, http://front.math.ucdavis.edu/ANT/ Your subscription will continue, unless you choose otherwise. I thank Dan Grayson for setting up the archives and his patient help with technical issues, and Michael and Greg for volunteering to take on this work. Nigel Boston http://www.math.wisc.edu/~boston/ Welcome to the preprint archives for papers in Algebraic Number Theory and Arithmetic Geometry. Use the Find facility of your browser on this page, or search: Our mirror site in the United Kingdom , set up by Richard Pinch. Our main site in the USA Instructions for authors Instructions for joining the mailing list . Members of the mailing list receive announcements of preprints when they are deposited in the archives. Some TeX fonts , stored in a tar image compressed with gzip, including the lams* and xy* fonts, which are needed for some of the preprints.

9. Sundry Algebraic Geometry And Commutative Algebra Sites A list of personal home pages. http://www.math.unl.edu/~bharbour/alggeom.html

I have compiled this list from a number of sources; if you know of addresses (your own or others) involving Algebraic Geometry or Commutative Algebra that I could include, please send me a note! Paolo Aluffi Kevin Coombes Duke archive Brian Harbourne ... Mika Seppala Mail Comments to: bharbourne@unl.edu

10. Algebraic Geometry Introduction to algebraic geometry. Learning the language. In order to get a feeling for what algebraic geometry is, let s to go through some examples. http://www.math.purdue.edu/~dvb/algeom.html

Introduction to Algebraic Geometry Math 665, fall 2001 Donu Arapura Blow up (If your browser supports mathml, then try this Introduction Books Software ... About this web page Learning the language In order to get a feeling for what algebraic geometry is, let's to go through some examples. Consider the space of 2x2 matrices over a field k with trace 0. These can be parameterized by 3-tuples (x,y,z) where x, y and z appear in the 11, 12, and 21 positions; therefore this can be identified with three dimensional affine space A . In these coordinates the determinant det(x,y,z) = -x -yz. The determinant is an algebraic map , and the fibers X t =det are algebraic subsets of A . These are in fact varieties since the polynomials -x -yz-t are irreducible for each t in k. Let's study the geometry of these sets. Suppose k= C , then I claim that X t is isomorphic to X whenever t is nonzero. To see this, choose a such that a = t, then the map (x,y,z) -> (ax,ay,az) defines an isomorphism between X and X t ; this can be checked by comparing coordinate rings.

11. Minicursos Do Centro De Análise Matemática, Geometria E Sistemas Dinâmicos - Held regularly at the Department of Mathematics, Instituto Superior T©cnico, Lisbon. http://www.math.ist.utl.pt/~jpnunes/istlectagp/

2003 - Vector Bundles on Curves and Generalized Theta Functions 2002 - Vector Bundles on Algebraic Curves 2000 - Conformal Field Theory The lectures are held at the Department of Mathematics of , Av. Rovisco Pais, Lisbon. ORGANIZATION Carlos Florentino Sponsored by the of

12. Coding Theory, Algebraic Geometry And Gröbner Bases D.A. Leonard. One in a series of snapshots of applications of discrete mathematics to other parts of mathematics. http://www.dms.auburn.edu/~rodgec1/cadcom/mathappl/leonsnap/leonsnap.html

One in a series of snapshots of applications of discrete mathematics to other parts of mathematics. D. A. Leonard Auburn University The Context The Problem The general decoding problem for any code, is to take a received word (that is, a corrupted code word) and produce (efficiently) the nearest code word to it (or equivalently the smallest error possible). For linear codes (subspaces), this is generally done by using functions of the received word which only depend on the error, not on the specific code word transmitted. Such functions are called syndromes For Reed-Solomon codes over , currently used in various applications such as CD technology, the syndromes are with the given received word, and a primitve element of One then uses a Berlekamp-Massey algorithm (or the extended Euclidean algorithm) to produce an error-locator polynomial (or an error-evaluator polynomial). Then one has a choice of producing all , (by viewing as a recurrence relation and the given syndromes as initial conditions) and using an inverse transform, with the (most likely) error or factoring , producing , and using Forney's formula: Algebraic-Geometric Codes Algebraic-geometric codes (the duals of those described in ``Coding Theory and Algebraic Geometry: An Interplay'') are generalizations of the Reed-Solomon codes above. As such, there should be an efficient decoding scheme that is modelled on the algorithm above. The first important algorithm in this process was the generalization of the Berlekamp-Massey algorithm to higher dimensions, published in the late 80's by Sakata. This lead to reasonably efficient vector-space based techniques, each with some flaws, either in the number of errors, number of points, or efficiency. The next important idea was published in 93 by Feng and Rao. This majority voting scheme allowed for production of more ``syndromes'' while row-reducing the syndrome matrix. Only recently has this been synthesized into a generalization of the above algorithm.

13. Journal Of Algebraic Geometry Number 1. Journal of algebraic geometry, The Journal of algebraic geometry is distributed by the American Mathematical Society for University Press, Inc. http://www.ams.org/jourcgi/jrnl_toolbar_nav/jag_all

Journals Home Search Author Info Subscribe ... Most recent issue Available Volumes and Issues Year Volume Issue Number 3 Number 2 Number 1 Year Volume Issue Number 4 Number 3 Number 2 Number 1 Year Volume Issue Number 4 Number 3 Number 2 Number 1 The Journal of Algebraic Geometry is distributed by the American Mathematical Society for University Press, Inc. Online ISSN 1534-7486; Print ISSN 1056-3911 Comments: jag-query@ams.org

14. Algebraic Areas Of Mathematics Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra. http://www.math.niu.edu/~rusin/known-math/index/tour_alg.html

Search Subject Index MathMap Tour ... Help! Algebraic Areas of Mathematics Return to start of tour Up to The Divisions of Mathematics The algebraic areas of mathematics developed from abstracting key observations about our counting, arithmetic, algebraic manipulations, and symmetry. Typically these fields define their objects of study by just a few axioms, then consider examples, structure, and application of these objects. We have included here the combinatorial topics and number theory ; each is arguably a distinctive area of mathematics but (as the MathMap suggests) these parts of mathematics, shown in shades of red, share definite affinities. The list on this page includes a rather large number of fields in the MSC scheme. It is also common to interpret the phrase "abstract algebra" in a more narrow sense - to view it as the fields obtained by adding successive axioms to describe the objects of study. Arguably then, abstract algebra is limited to sections 20 and 22 (Group Theory), 13, 16, and 17 (Ring Theory), 12 (Field Theory), and 15 (Linear Algebra), taken in this way as a succession from fewest to most restrictive sets of axioms. The use of algebra is pervasive in mathematics. This particularly true of group theory - symmetry groups arise very naturally in almost every area of mathematics. For example, Klein's vision of geometry was essentially to reduce it to a study of the underlying group of invariants; Lie groups first arose from Lie's investigations of differential equations. It is also true of linear algebra - a field which, properly construed, includes huge portions of Numerical Analysis and Functional Analysis, for example hence that field's central position in the MathMap.

15. Algebraic Geometry A. Grothendieck's S©minaire de G©ometrie Alg©brique produced by F. Calegari, J. Borger and W. Stein. JPEG scans of typewritten material. http://modular.fas.harvard.edu/sga/sga/

Séminaire de Géometrie Algébrique (About this project) More About Grothendieck and Other Versions of the Scans Grothendieck View all user annotations (new) Revêtements étales et groupe fondamental Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux Schémas en groupes I: Propriétés générales des schémas en groupes ... Groupes de monodromie en géométrie algébrique II View some pictures of Grothendieck . There are some other scans of SGA and EGA

16. Algebraic Geometry -- From MathWorld algebraic geometry. This entry contributed by Todd Rowland. algebraic geometry is the study of geometries that come from algebra, in particular, from rings. http://mathworld.wolfram.com/AlgebraicGeometry.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Algebra Algebraic Geometry Abstract Algebraic Curves ... Rowland Algebraic Geometry This entry contributed by Todd Rowland Algebraic geometry is the study of geometries that come from algebra, in particular, from rings . In classical algebraic geometry , the algebra is the ring of polynomials , and the geometry is the set of zeros of polynomials, called an algebraic variety . For instance, the unit circle is the set of zeros of and is an algebraic variety , as are all of the conic sections In the twentieth century, it was discovered that the basic ideas of classical algebraic geometry can be applied to any commutative ring with a unit, such as the integers . The geometry of such a ring is determined by its algebraic structure, in particular its prime ideals . Grothendieck defined schemes as the basic geometric objects, which have the same relationship to the geometry of a ring as a

17. Preprints.html Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript. http://www.math.lsa.umich.edu/~idolga/lecturenotes.html

Lecture Notes Enriques surfaces I: Corrections ( ps pdf LECTURES ON INVARIANT THEORY ( ps pdf INTRODUCTION TO PHYSICS Part 1 ( ps pdf Part 2 ( ps pdf Part 3 ( ps pdf Part 4 ( ps pdf Literature ( ps pdf MODULAR FORMS ( pdf INTRODUCTION TO ALGEBRAIC GEOMETRY Lectures 1-17 ( ps INTRODUCTION TO STRING THEORY Lectures 1-8( ps pdf TOPICS IN CLASSICAL ALGEBRAIC GEOMETRY. PART I Chapters 1-8( pdf TOPICS IN CLASSICAL ALGEBRAIC GEOMETRY. PART II Chapters 9- ( pdf

18. AC Commutative Algebra Articles cover commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics. http://front.math.ucdavis.edu/math.AC

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ AC Commutative Algebra Calendar Search Authors: AB CDE FGH IJK ... U-Z New articles (last 12) 4 Jun math.AC/0406057 Gorenstein projective dimension for complexes. Oana Veliche AC RA 28 May math.AC/0405526 Semi-dualizing modules and related Gorenstein homological dimensions. Henrik Holm , Peter Jorgensen . 25 pages. AC 28 May math.AC/0405523 Cohen-Macaulay injective, projective, and flat dimension. Henrik Holm , Peter Jorgensen . 18 pages. AC 27 May math.AC/0405499 Associated primes and cofiniteness of local cohomology modules. Mohammad T. Dibaei , Siamak Yassemi . 9 pages. AC Cross-listings 28 May math.AT/0405525 Andrew Baker , Birgit Richter . 6 pages. Glasgow University Mathematics Department preprint no. 04/20. AT AC 27 May math.CV/0405491 La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes. Martin Weimann . 33 pages. CV AC 27 May math.CO/0405490 The ring of multisymmetric functions. F. Vaccarino . 12 pages. CO AC RT 25 May math.AG/0405464 Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz fnctions. Holger Brenner , Georg Hein AG AC Revisions 2 Jun math.AC/0405499

19. Arithmetic Algebraic Geometry Developing powerful methods taken from geometry to study the arithmetical properties of algebraic equations. Previous network in arithmetic algebraic geometry. http://www.arithgeom-network.univ-rennes1.fr/

A Research Training Network of the European Union Overview Partners Programme Positions Activities Project overview Developing powerful methods taken from geometry to study the arithmetical properties of algebraic equations Algebraic equations and their arithmetical properties have interested mankind since antiquity. One has only to think of the works of Pythagoras and Diophantus, which were a milestone in their time. For many centuries such problems have fascinated both serious mathematicians (Fermat, Gauss, ...) and amateurs alike. However, developments in recent years have transformed the subject into one of the central areas of mathematical research, which has relations with, or applications to, virtually every mathematical field, as well as an impact to contemporary everyday life (for example, the use of prime numbers and factorisation for encoding "smart" cards). The classical treatment of equations by analysis and geometry in the realm of complex numbers in this century has found a counterpart, in the similar theories over finite and p -adic fields, which have particular significance for arithmetic questions. The study of certain functions encoding arithmetic information and generalising the Riemann zeta-function (

20. MSRI - Henri Gillet Slides in multimedia format from a lecture by Henri Gillet at MSRI. http://www.msri.org/publications/ln/msri/1998/mtf/gillet/1/

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