Durham Medical Books > Algebraic Geometry > Read e-book online Algebraic geometry I. Algebraic curves, manifolds, and PDF

Read e-book online Algebraic geometry I. Algebraic curves, manifolds, and PDF

By I. R. Shafarevich

ISBN-10: 0387519955

ISBN-13: 9780387519951

This quantity of the Encyclopaedia comprises components. the 1st is dedicated to the speculation of curves, that are handled from either the analytic and algebraic issues of view. beginning with the elemental notions of the idea of Riemann surfaces the reader is lead into an exposition protecting the Riemann-Roch theorem, Riemann's primary lifestyles theorem, uniformization and automorphic services. The algebraic fabric additionally treats algebraic curves over an arbitrary box and the relationship among algebraic curves and Abelian forms. the second one half is an advent to higher-dimensional algebraic geometry. the writer offers with algebraic types, the corresponding morphisms, the idea of coherent sheaves and, eventually, the speculation of schemes. This booklet is a really readable advent to algebraic geometry and should be immensely worthwhile to mathematicians operating in algebraic geometry and intricate research and particularly to graduate scholars in those fields.

Show description

Read or Download Algebraic geometry I. Algebraic curves, manifolds, and schemes PDF

Similar algebraic geometry books

Get Moduli of Supersingular Abelian Varieties PDF

Abelian types may be categorized through their moduli. In confident attribute the constitution of the p-torsion-structure is an extra, great tool. For that constitution supersingular abelian kinds might be thought of the main particular ones. they supply a place to begin for the high-quality description of assorted constructions.

Download e-book for iPad: Algebraic Integrability, Painlevé Geometry and Lie Algebras by Mark Adler

From the reports of the 1st edition:"The target of this publication is to provide an explanation for ‘how algebraic geometry, Lie concept and Painlevé research can be utilized to explicitly clear up integrable differential equations’. … one of many major benefits of this ebook is that the authors … succeeded to give the cloth in a self-contained demeanour with quite a few examples.

Read e-book online Measure, Topology, and Fractal Geometry PDF

In response to a path given to gifted high-school scholars at Ohio college in 1988, this publication is basically a complicated undergraduate textbook concerning the arithmetic of fractal geometry. It properly bridges the distance among conventional books on topology/analysis and extra really expert treatises on fractal geometry.

Download e-book for kindle: Elliptic Curves: Function Theory, Geometry, Arithmetic by Henry McKean, Victor Moll

The topic of elliptic curves is without doubt one of the jewels of nineteenth-century arithmetic, whose masters have been Abel, Gauss, Jacobi, and Legendre. This publication offers an introductory account of the topic within the kind of the unique discoverers, with references to and reviews approximately newer and sleek advancements.

Extra resources for Algebraic geometry I. Algebraic curves, manifolds, and schemes

Example text

Soit C une courbe lisse sur F, soit A l’anneau local de C en un point ferm´e de corps r´esiduel E, soit X un A-sch´ema r´egulier, propre et plat sur A, a` fibre g´en´erique X /K lisse, a` fibre sp´eciale un diviseur Y /E a` croisements normaux stricts. Si X est une K-vari´et´e s´eparablement rationnellement connexe, alors il existe une composante r´eduite Yi de Y qui est g´eom´etriquement irr´eductible sur E. 10 vaut plus g´en´eralement lorsque la fibre g´en´erique est une vari´et´e rationnellement connexe.

De Jong et Starr (travaux en cours) ont obtenu une s´erie de r´esultats sur les intersections compl`etes lisses dans l’espace projectif. Pour simplifier, je cite leurs r´esultats pour les hypersurfaces. 6 (de Jong-Starr) [43] Une hypersurface lisse de degr´e d ≥ 2 dans PnC avec n ≥ d2 − 1 est rationnellement simplement connexe, a` l’exception des quadriques dans P3C . 7 (de Jong-Starr) [43] Une hypersurface lisse de degr´e d ≥ 2 dans PnC avec n ≥ 2d 2 − d − 1 est fortement rationnellement simplement connexe.

On est sur un corps de nombres k, X et Y sont deux k-vari´et´es lisses g´eom´etriquement int`egres, la k-vari´et´e Y est projective, on a un k-morphisme projectif f : X → Y de fibre g´en´erique g´eom´etriquement int`egre. On note U ⊂ X l’ouvert de lissit´e du morphisme f . On demande quels sont les liens entre la g´eom´etrie du morphisme f et les propri´et´es de surjectivit´e des applications induites X(kv ) → Y (kv ) pour presque toute place v, ou d´ej`a pour une infinit´e de places v du corps de nombres k.

Download PDF sample

Algebraic geometry I. Algebraic curves, manifolds, and schemes by I. R. Shafarevich

by Robert

Rated 4.37 of 5 – based on 49 votes