Injectivity Theorems with Multiplier Ideal Sheaves and Their Applications

2015/01/01 by Shin-ichi Matsumura
Mathematics · #Algebraic Geometry and Number Theory #Conjecture #Extension (predicate logic) #Geometry and complex manifolds #Harmonic #Holomorphic and Operator Theory #Ideal (ethics) #Multiplier (economics) #Type (biology) #math.AG #math.CV #math.DG #msc:14F18 #msc:32L10 #msc:32L20

paper · pdf · doi:10.1007/978-4-431-55744-9_18

published as The Proceedings volume of KSCV10, Volume 144 of the series Springer Proceedings in Mathematics & Statistics pp 241--255, 06 August 2015 · 14pages. arXiv admin note: substantial text overlap with arXiv:1406.6132, arXiv:1308.2033

openalex publication_date 2015/01/01 · arxiv created 2015/11/13 · arxiv updated 2015/11/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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 L²-method for the dbar-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).

Citations

• Versions of injectivity and extension theorems
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities
• Lectures on Vanishing Theorems
• Birational Geometry of Algebraic Varieties
• Vanishing Theorems on Complete Kähler Manifolds
• Existence of minimal models for varieties of log general type