Extension of log pluricanonical forms from subvarieties

Abstract

In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which relates the positivities of canonical bundle of the ambient projective manifold and that of the (maximal) center of log canonical singularities. This is an extension of the corresponding result in my previous work where I dealt with log pluricanonical systems of general type. This subadjunction theorem indicates an approach to solve the abundance conjecture for canonical divisors (or log canonical divisors) in terms of the induction in dimension.

numerous typos corrected, minor change of the statements

References in corpus (4)

• Invariance of Plurigenera
• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Pluricanonical systems of projective varieties of general type
• Dynamical construction of Kähler-Einstein metrics

Cited by in corpus (7)

• Numerical dimension and a Kawamata-Viehweg-Nadel type vanishing theorem on compact Kähler manifolds
• Bergman kernels and subadjunction
• A Bergman kernel proof of the Kawamata subadjunction theorem
• Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature
• Global generation of the direct images of relative pluricanonical systems
• $L^2$ extension of adjoint line bundle sections
• Extensions of multiply twisted pluri-canonical forms