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A CANONICAL BUNDLE FORMULA
A higher dimensional analogue of Kodaira’s canonical bundle formula is obtained. As applications, we prove that the log-canonical ring of a klt pair with κ ≤ 3is finitely generated, and that thereExpand
Abundance theorem for semi log canonical threefolds
0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 1. Definitions and preliminaries . . . . . . . . . . . . . . .Expand
HIGHER DIMENSIONAL ALGEBRAIC GEOMETRY
I will talk about termination of flips in dimension 4 following AHacon-Kawamata and the work of Shokurov since then.
Introduction to the log minimal model program for log canonical pairs
We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Koll\'ar's vanishing and torsion-free theorems for embedded simple normalExpand
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.
Semi-stable minimal model program for varieties with trivial canonical divisor
We give a sufficient condition for the termination of flips. Then we discuss a semi-stable minimal model program for varieties with (numerically) trivial canonical divisor as an application. We alsoExpand
Finite generation of the log canonical ring in dimension four
We treat two different topics on the log minimal model program, especially for four-dimensional log canonical pairs. (a) Finite generation of the log canonical ring in dimension four. (b) AbundanceExpand
Smooth projective toric varieties whose nontrivial nef line bundles are big
For any n > 3, we explicitly construct smooth projective toric n-folds of Picard number ≥ 5, where any nontrivial nef line bundles are big.
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