代数曲线几何-第1卷

本书特色

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阿尔巴雷洛所著的《代数曲线几何》是一部讲述代数曲线几何的专著,分为上下两册,内容综合,全面,自成体系。本书是这部专著的上册,运用抽象代数几何技巧讲述了代数曲线几何的深层次结果,每章末都有文献材料说明和练习,可以帮助读者了解原始背景和发展过程,已达到更好理解书中的理论的目的。读者对象:数学专业的所有对代数曲线几何感兴趣的学生和科研人员。

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目录

guide for the readerlist of symbolschapter ipreliminariesl. divisors and line bundles on curves2. the riemann-roch and duality theorems3. abel’s theorem4. abelian varieties and the theta function5. poincar6’s formula and riemann’s theorem6. a few words about modulibibliographical notesexercises a. elementary exercises on plane curves b. projections c. ramification and plucker formulas d. miscellaneous exercises on linear systems e. weierstrass points f. automorphisms g. period matrices h. elementary properties of abelian varietiesappendix athe riemann-roch theorem, hodge theorem, andadjoint linear systemsl. applications of the discussion about plane curves with nodes2. adjoint conditions in generalchapter 11determinantal varieties1. tangent cones to analytic spaces2. generic determinantal varieties: geometric description3. the ideal of a generic determinantal variety4. determinantai varieties and porteous’ formula (i) sylvester’s determinant (ii) the top chern class of a tensor product (iii) porteous’ formula (iv) what has been proved5. a few applications and examples bibliographical notes exercises a. symmetric bilinear maps b. quadrics c. applications of porteous’ formula d. chern numbers of kernel bundleschapter i11introduction to special divisors1. clifford’s theorem and the general position theorem2. castelnuovo’s bound, noether’s theorem, and extremal curves3. the enriques-babbage theorem and petri’s analysis of the canonical ideal bibliographical notes exercises a. symmetric products of pi b. refinements of clifford’s theorem c. complete intersections d. projective normality (i) e. castelnuovo’s bound on k-normality f. intersections of quadrics g. space curves of maximum genus h. g. gherardelli’s theorem i. extremal curves j. nearly castelnuovo curves k. castelnuovo’s theorem l. secant planeschapter ivthe varieties of special linear series on a curve1. the brili-noether matrix and the variety c,2. the universal divisor and the poincar6 line bundles3. the varieties w[(c) and g(c) parametrizing special linear series on a curve4. the zariski tangent spaces to g(c) and w(c)5. first consequences of the infinitesimal study of gc) and wc) biographical notes exercises a. elementary exercises on 0 b. an interesting identification c. tangent spaces to wt(c) d. mumford’s theorem for.qj’s e. martens-mumford theorem for birational morphisms f. linear series on some complete intersections g. keem’s theoremschapter vthe basic results of the brill-noether theory bibliographical notes exercises a. w (c) on a curve c of genus 6 b. embeddings of small degree c. projective normality (ii) d. the difference map oa: cd x cd -, j(c) (i)chapter vithe geometric theory of riemann’s theta function1. the riemann singularity theorem2. kempf’s generalization of the riemann singularity theorem3. the torelli theorem4. the theory of andreotti and mayer bibliographical notes exercises a. the difference map o (ii) b. refined torelli theorems c. translates of wo- 1, their intersections, and the toreili theorem d. prill’s problem e. another proof of the torelli theorem f. curves of genus 5 g. accola’s theorem h. the difference map a (lli) i. geometry of the abelian sum map u in low generaappendix btheta characteristics1. norm maps2. the weil pairing3. theta characteristics4. quadratic forms over z/2appendix cprym varieties exerciseschapter vllthe existence and connectedness theorems for pwd(c)1. ample vector bundles2. the existence theorem3. the conneetedness theorem4. the class of w,(c)5. the class of c bibliographical notes exercises a. the connectedness theorem b. analytic cohomology of cd, d < 2g - 2 c. excess linear serieschapter viiienumerative geometry of curves1. the grothendieck-riemann-roch formula2. three applications of the grothendicck-riemann-roch formula3. the secant plane formula: special cases4. the general secant plane formula5. diagonals in the symmetric product bibliographical notes exercises a. secant planes to canonical curves b. weierstrass pairs c. miscellany d. push-pull formulas for symmetric products e. reducibility of wg-l n (wg-1 + u) (ii) f. every curve has a base-point-free g1- 1bibliographyindex

封面

代数曲线几何-第1卷

书名:代数曲线几何-第1卷

作者:阿尔巴雷洛

页数:386

定价:¥69.0

出版社:世界图书出版公司

出版日期:2014-05-01

ISBN:9787510075902

PDF电子书大小:87MB 高清扫描完整版

百度云下载:http://www.chendianrong.com/pdf

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