标题：代数几何中的解析方法
图书信息
出版社: 高等教育出版社; 第1版 (2010年9月1日)
外文书名: Analytic Methods in Algebraic Geometry
精装: 231页
正文语种: 英语
开本: 16
ISBN: 9787040305319
条形码: 9787040305319
尺寸: 24.2 x 17 x 1.6 cm
重量: 481 g
作者简介
作者：（法国）德马依（Jean-Pierre Demailly）
内容简介
《代数几何中的解析方法(英文版)》内容简介：This volume is an expansion of lectures given by the author at the Park City Mathematics Institute in 2008 as well as in other places. The main purpose of the book is to describe analytic techniques which are useful to study questions such as linear series, multiplier ideals and vanishing theorems for algebraic vector bundles. The exposition tries to be as condensed as possible, assuming that the reader is already somewhat acquainted with the basic concepts pertaining to sheaf theory,homological algebra and complex differential geometry. In the final chapters, some very recent questions and open problems are addressed, for example results related to the finiteness of the canonical ring and the abundance conjecture, as well as results describing the geometric structure of Kahler varieties and their positive cones.
目录
introduction 
chapter 1. preliminary material: cohomology, currents 
1.a. dolbeault cohomology and sheaf cohomology 
1.b. plurisubharmonic functions 
1.c. positive currents 
chapter 2. lelong numbers and intersection theory 
2.a. multiplication of currents and monge-ampere operators 
2.b. lelong numbers 
chapter 3. hermitian vector bundles, connections and curvature 
chapter 4. bochner technique and vanishing theorems 
4.a. laplace-beltrami operators and hodge theory 
4.b. serre duality theorem 
4.cbochner-kodaira-nakano identity on kahler manifolds 
4.d. vanishing theorems 
chapter 5. l2 estimates and existence theorems 
5.a. basic l2 existence thcorcms 
5.b. multiplier ideal sheaves and nadel vanishing theorem 
chapter 6. numerically effective andpseudo-effective line bundles 
6.a. pseudo-effcctive line bundles and metrics with minimal singularities 
6.b. nef line bundles 
6.c. description of thc positive cones. 
6.d. the kawamata-viehweg vanishing theorem 
6.e. a uniform global generation property due to y.t. siu 
chapter 7. a simple algebraic approach to fujita's conjecture 
chapter 8. holomorphic morse inequalities 
8.a. general analytic statement on compact complex manifolds 
8.b. algebraic counterparts of the holomorphic morse inequalities 
8.c. asymptotic cohomology groups 
8.d. transcendental asymptotic cohomology unctions 
chapter 9. effective version of matsusaka's big theorem 
chapter 10. positivity concepts for vector bundles 
chapter 11. skoda's l2 estimates for surjective bundle morphisms 
11.a. surjectivity and division theorems 
11.b. applications to local algebra: the briancon-skoda theorem 
chapter 12. the ohsawa-takegoshi l2 extension theorem 
12.a. the basic a priori inequality 
12.b. abstract l2 existence theorem for solutions of0-equations 
12.c. the l2 extension theorem 
12.d. skoda's division theorem for ideals of holomorphic functions 
chapter 13. approximation of closed positive currents by analytic cycles 
13.a. approximation of plurisubharmonic functions via bergman kernels 
13.b. global approximation of closed (1,1)-currents on a compact complex manifold 
13.c. global approximation by divisors 
13.d. singularity exponents and log canonical thresholds 
13.e. hodge conjecture and approximation of (p, p)- currents 
chapter 14. subadditivity of multiplier ideals and fujita's approximate zariski decomposition 
chapter 15. hard lefschetz theorem 
with multiplier ideal sheaves 
15.a. a bundle valued hard lefsehetz theorem 
15.b. equisingular approximations of quasi plurisubharmonic functions 
15.c. a bochner type inequality 
15.d. proof of theorem 15.1 
15.e. a counterexample 
chapter 16. invariance of plurigenera of projective varieties 
chapter 17. numerical characterization of the kahler cone 
17.a. positive classes in intermediate (p, p)-bidegrees 
17.b. numerically positive classes of type (1,1) 
17.c. deformations of compact kahler manifolds 
chapter 18. structure of the pseudo-effective cone and mobile intersection theory 
18.a. classes of mobile curves and of mobile (n- 1,n- 1)-currents 
18.b. zariski decomposition and mobile intersections 
18.c. the orthogonality estimate 
18.d. dual of the pseudo-effective cone 
18.e. a volume formula for algebraic (1,1)-classes on projective surfaces 
chapter 19. super-canonical metrics and abundance 
19.a. construction of super-canonical metrics 
19.b. invariance of plurigenera and positivity of curvature of super-canonical metrics 
19.c. tsuji's strategy for studying abundance 
chapter 20. siu's analytic approach and paun's non vanishing theorem 
references