Vanishing and injectivity theorems for LMMP

Abstract

This preprint has been withdrawn. It is because I will never publish this preprint since everything has been contained in my new preprint: arXiv:0907.1506. Please refer to arXiv:0907.1506. Please do not cite this preprint any more.

v2: introduction was expanded, minor revisions, v3: this preprint has been withdrawn. everything has been contained in arXiv:0907.1506

References in corpus (5)

• Quasi-log varieties
• Basic properties of log canonical centers
• A transcendental approach to Kollár's injectivity theorem II
• A transcendental approach to Kollár's injectivity theorem
• Base point free theorems--saturation, b-divisors, and canonical bundle formula--

Cited by in corpus (7)

• Introduction to the log minimal model program for log canonical pairs
• The canonical sheaf of Du Bois singularities
• Introduction to the theory of quasi-log varieties
• Effective base point free theorem for log canonical pairs--Kollár type theorem
• Fundamental properties of basic slc-trivial fibrations, II
• Vanishing theorems for toric polyhedra
• Notes on the log minimal model program