Multiplier ideal sheaves in complex and algebraic geometry

被引：50

作者：

Siu, YT ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2005年 / 48卷 / Suppl 1期

关键词：

algebraic geometry; multiplier ideal sheaf; effective problem; invariance of plurigenera; canonical ring; minimal model; complex Monge-Ampere equation; complex Neumann estimate; weakly pseudoconvex domain;

D O I：

10.1007/BF02884693

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed. Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.

引用

页码：1 / 31

页数：31

共 50 条

[11] Coherence of multiplier ideal sheaves with estimates.
Popovici, D
COMPTES RENDUS MATHEMATIQUE, 2004, 338 (02) : 151 - 156
[12] Injectivity Theorems with Multiplier Ideal Sheaves and Their Applications
Matsumura, Shin-ichi
COMPLEX ANALYSIS AND GEOMETRY, KSCV 10, 2015, 144 : 241 - 255
[13] Multiplier ideals in algebraic geometry
Grushevsky, S
Snowbird Lectures in Algebraic Geometry, 2005, 388 : 89 - 106
[14] RELATIVE BERTINI TYPE THEOREM FOR MULTIPLIER IDEAL SHEAVES
Fujino, Osamu
OSAKA JOURNAL OF MATHEMATICS, 2023, 60 (01) : 207 - 226
[15] A short note on multiplier ideal sheaves on singular varieties
Wessler, M
INTERNATIONAL JOURNAL OF MATHEMATICS, 2003, 14 (04) : 361 - 369
[16] Multiplier ideal sheaves and the Kahler-Ricci flow
Phong, D. H.
Sesum, Natasa
Sturm, Jacob
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2007, 15 (03) : 613 - 632
[17] BUILDING A MODEL CATEGORY OUT OF MULTIPLIER IDEAL SHEAVES
Lee, Seunghun
THEORY AND APPLICATIONS OF CATEGORIES, 2017, 32 : 437 - 487
[18] EFFECTIVE LOCAL FINITE GENERATION OF MULTIPLIER IDEAL SHEAVES
Popovici, Dan
ANNALES DE L INSTITUT FOURIER, 2010, 60 (05) : 1561 - 1594
[19] A complex Frobenius theorem, multiplier ideal sheaves and Hermitian- Einstein metrics on stable bundles
Weinkove, Ben
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (04) : 1577 - 1592
[20] Characterization of multiplier ideal sheaves with weights of Lelong number one
Guan, Qi'an
Zhou, Xiangyu
ADVANCES IN MATHEMATICS, 2015, 285 : 1688 - 1705

← 1 2 3 4 5 →