1. Home Page J. S. Milne. Includes preprints and course notes on Group Theory, Fields and Galois Theory, algebraic geometry, Algebraic Number Theory,Modular Functions and Modular http://www.jmilne.org/math/

2. Algebraic Geometry In order to get a feeling for what algebraic geometry is, let s to go through some For doing calculations in algebraic geometry and commutative algebra, 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.

3. 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: October 18, 2004) 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 Multiplier ideal sheaves and analytic methods in algebraic geometry , Lecture Notes, School on Vanishing theorems and effective results in Algebraic Geometry, ICTP Trieste, Avril 2000 (dvi) Fonctions holomorphes et surfaces de Riemann, vc.ps.gz Lectures, large audience papers

4. Arithmetic Algebraic Geometry A European network of 12 working groups from 6 countries. 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 (

5. Algebraic Geometry Some information about algebraic geometry and geometers. 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.

6. Southwestern Center Home Based at the University of Arizona, in collaboration with the Universities of New Mexico, Southern California, and Texas. Annual conference. http://swc.math.arizona.edu/

Southwestern Center for Arithmetical Algebraic Geometry The Upcoming Arizona Winter School Previous Arizona Winter Schools Our Distinguished Lecture Series Notes and Other Documents ... A Slide Show (Requires Javascript) About the Southwestern Center Local and Travel Information Site Map and Search E-mail us News pdf The Southwestern Center The Southwestern Center for Arithmetical Algebraic Geometry was founded in 1997 by seven mathematicians working in the southwest, namely Alex Buium, Minhyong Kim, Bill McCallum, Wayne Raskind, Dinesh Thakur, Doug Ulmer (PI), and Felipe Voloch. They were joined in 2002 by Michael Nakamaye, Bjorn Poonen, and Fernando Rodriguez-Villegas. The Center is funded by the National Science Foundation, and its activities include the annual Arizona Winter School and a distinguished lecture series. Follow the links at left to learn more about the Southwestern Center. Updates To receive occasional messages with news about the Southwestern Center, join our mailing list by filling out this form Site last updated: May 2, 2005

7. Algebraic Geometry, Commutative Algebra And Combinatorics -- Erice 2001, NATO Ad Exterior Algebra Methods and Other New Directions. Erice, Sicily, Italy; 9 15 September 2001. http://www.math.sunysb.edu/~sorin/Erice-2001/

Event photos The workshop in Erice will address a wide range of new developments in classical Algebraic Geometry such as curves and their moduli, surfaces, higher dimensional varieties, vector bundles, and toric varieties. A special focus will be on exterior algebra methods which have recently grown in importance in Algebraic Geometry, Commutative Algebra, and Combinatorics, and their computational aspects (Bernstein-Gel'fand-Gel'fand correspondence, Beilinson monad, theory of Chow forms and resultants, algebraic shifting, free resolutions over the exterior algebra, linear syzygies, hyperplane arrangements, ...) Organizing Committee: David Eisenbud Lucian Badescu Sorin Popescu and Alfio Ragusa Speakers (tentative): The following people have responded positively to our invitation: Sponsors: NATO Scientific Affairs Division EAGER: European Algebraic Geometry Research Training Network and the University of Catania , Sicily. Registration: The cost of staying at the Ettore Majorana Centre will be approximately $80 per night (lodging/meals/transfer from/to the airport/1/2 day trip included), and there will be a fee of $100 for the social events. We will be able to offer financial assistance to some of the participants, particularly to younger mathematicians and speakers.

8. 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/

9. Algebraic Geometry Some information about algebraic geometry and geometers http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. 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

11. Journal Of Algebraic Geometry Online Tables of contents, abstracts and references from vol.11 (2002). Full text to subscribers (TeX, DVI, PDF, PS). 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. Submission information can be found on the journal's Initial Submissions page.

12. Algebraic Number Theory Archives Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Journal Of Algebraic Geometry Journal of algebraic geometry. The Journal of algebraic geometry is distributed by the American Mathematical Society 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 4 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 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. Macaulay 2 Home Page A new software system devoted to supporting research in algebraic geometry and commutative algebra. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Algebraic Geometry -- From MathWorld algebraic geometry is the study of geometries that come from algebra, As a consequence, algebraic geometry became very useful in other areas of http://mathworld.wolfram.com/AlgebraicGeometry.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Algebra Algebraic Geometry Abstract Algebraic Curves ... Rowland, Todd Algebraic Geometry 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 manifold to a coordinate chart . The language of category theory evolved at around the same time, largely in response to the needs of the increasing abstraction in algebraic geometry.

16. 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.

17. Algebraic Geometry Algebraic number theory, Class field theory, algebraic geometry, Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. The Algebraic Geometry Notebooks For Non-Experts By Aksel Sogstad. Short introductory sketch of some topics in the algebraic geometry of curves. http://www.geocities.com/akselsogstad/algnotes/

The Algebraic Geometry Notebooks For Non-Experts By Aksel Sogstad These pages has moved to www.sogstad.net/algnotes. Please click!

19. EAGER - European Algebraic Geometry Research Training Network European algebraic geometry research training network. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

20. 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 ( 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 ( pdf INTRODUCTION TO STRING THEORY Lectures 1-8( ps pdf TOPICS IN CLASSICAL ALGEBRAIC GEOMETRY Chapters 1-11( pdf

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