A Bergman kernel proof of the Kawamata subadjunction theorem

Inversion of subadjunction and multiplier ideals

We present a generalization of the multiplier ideal version of inversion of adjunction, often known as the restriction theorem, to centers of arbitrary codimension. We approach inversion of adjunction from the subadjunction point of view. Let X be a smooth complex projective variety and let Z be an exceptional log-canonical center of an effective Q-divisor D on some dense open subset of X that contains the generic point of Z. Any subvariety of X can be expressed as such a center for some D. We define an adjoint ideal that measures how non-klt (X, D) is outside the generic point of Z. Our main …

Bergman kernels and subadjunction

In this article our main result is a more complete version of the statements obtained in {\rm [6]}. One of the important technical point of our proof is an $\displaystyle L^{2\over m}$ extension theorem of Ohsawa-Takegoshi type, which is derived from the original result by a simple fixed point method. Moreover, we show that these techniques combined with an appropriate form of the"invariance of plurigenera" can be used in order to obtain a new proof of the celebrated Y. Kawamata subadjunction theorem.

Extension of log pluricanonical forms from subvarieties

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 ca…

关于广义Kaehler对的典范丛公式与伴随性质

On the Canonical Bundle Formula and Adjunction for Generalized Kaehler Pairs

该研究针对Kaehler簇上的广义对，证明了典范丛公式、次伴随及伴随逆定理的类比结果，推导了BDPP猜想与锥定理的关联，并完善了已有相关结论。

Variation of Bergman kernels of adjoint line bundles

Generalizing the recent result of Berndtsson, we prove the Nakano semipositivity of the direct image of relative pluricanonical systems and the direct image of relative adjoint (singular) hermitian line bundle with semipositive curvature. This gives a new proof of Kawamata's theorem on the semipositivity of the direct image of relative pluricanonical systems.

Introduction to the Minimal Model Program and the existence of flips

The first aim of this note is to give a concise, but complete and self-contained, presentation of the fundamental theorems of Mori theory - the nonvanishing, base point free, rationality and cone theorems - using modern methods of multiplier ideals, Nadel vanishing, and the subadjunction theorem of Kawamata. The second aim is to write up a complete, detailed proof of existence of flips in dimension n assuming the minimal model program with scaling in dimension n-1.