Extension of log pluricanonical forms from subvarieties

Details Extension of log pluricanonical forms from subvarieties Extension of log pluricanonical forms from subvarieties

2007-09-17

arxiv.org/abs/0709.2710v2

Mathematics

Algebraic Geometry

numerous typos corrected, minor change of the statements

Scientific paper

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.

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