Osamu Fujino

Fundamental Theorems for the Log Minimal Model Program

In this paper, we prove the cone theorem and the contraction theorem for pairs (X;B), where X is a normal variety and B is an effective R-divisor on X such that KX +B is R-Cartier.

Abundance theorem for semi log canonical threefolds

0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 1. Definitions and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 2. Reduced boundaries of dlt n-folds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 3. Finiteness of B-pluricanonical representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 4. The abundance theorem for slc threefolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

Fundamental theorems for semi log canonical pairs

We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log canonical pairs.

Minimal Model Theory for Log Surfaces

We discuss the log minimal model program for log surfaces. We show that the minimal model program for surfaces works under much weaker assumptions than we expected.

Log pluricanonical representations and the abundance conjecture

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is semi-ample if and only if so is the log canonical divisor of its normalization. We also treat many other applications.

Variations of Mixed Hodge Structure and Semipositivity Theorems

We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove a generalization of the Fujita–Kawamata semi-positivity theorem.

On Kawamata’s theorem

In this paper, we discuss a proof of existence of log minimal models or Mori fibre spaces for klt pairs

Theory of non-lc ideal sheaves: Basic properties

(X/Z,B)

Non-vanishing theorem for log canonical pairs

with

Finite generation of the log canonical ring in dimension four

B