Yoshinori Gongyo

Characterization of varieties of Fano type via singularities of Cox rings

We show that every Mori dream space of globally F- regular type is of Fano type. As an application, we give a charac- terization of varieties of Fano type in terms of the singularities of their Cox rings.

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.

Reduction maps and minimal model theory

We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a klt pair

Abundance theorem for numerically trivial log canonical divisors of semi-log canonical pairs

(X,\Delta)

On weak Fano varieties with log canonical singularities

can be detected on the base of the

Kollár’s injectivity theorem for globally F -regular varieties

(K_{X}+\Delta)

On canonical bundle formulaS and subadjunctions

-trivial reduction map. Thus we show that the main conjectures of the minimal model program can be interpreted as a natural statement on the existence of curves on

On images of weak Fano manifolds

X

On the Minimal Model Theory for DLT Pairs of Numerical Log Kodaira Dimension Zero

.

Versions of injectivity and extension theorems

We prove the abundance theorem for numerically trivial log canonical divisors of log canonical pairs and semi-log canonical pairs.