Injectivity Theorems with Multiplier Ideal Sheaves and Their Applications

被引：7
|
作者：
Matsumura, Shin-ichi [1 ]
机构：
[1] Tohoku Univ, Math Inst, Aoba Ku, 6-3 Aramaki Aza Aoba, Sendai, Miyagi 9808578, Japan
来源：
COMPLEX ANALYSIS AND GEOMETRY, KSCV 10 | 2015年 / 144卷
关键词：
Injectivity theorems; Vanishing theorems; Singular metrics; Multiplier ideal sheaves; The theory of harmonic integrals; L-2-methods; Extension theorems; Abundance conjecture; COMPACT KAHLER-MANIFOLDS; POSITIVE SCALAR CURVATURE; NADEL VANISHING THEOREM; LINE BUNDLES; EINSTEIN METRICS; ABUNDANCE THEOREM; MINIMAL MODELS; EXISTENCE; THREEFOLDS; CONJECTURE;
D O I：
10.1007/978-4-431-55744-9_18
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L-2-method for the.-equation and the theory of harmonic integrals. As applications, we obtain Nadel type vanishing theorems and extension theorems for pluri-canonical sections of log pairs. Moreover, we give some results on semi-ampleness related to the abundance conjecture in birational geometry (the minimal model program).
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页码：241 / 255
页数：15
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