On a topological space, algebraic topology and homological
algebra endow cohomology groups with various filtrations. In the
case of algebraic varieties, one may wonder if such filtrations,
e.g. the Grothendieck filtration, the Leray filtration, the...
The method of multiplier ideals is one of the most versatile
tools to study singularities of varieties. For the local theory, we
present a connection between multiplier ideals and D-modules based
on joint work with M. Mustata and M. Saito which has...
Main conjectures of (log) MMP are: A) existence of flips, B)
termination of flips, and C) finite generation, all of which were
settled by 1992 in dim 3 by Mori, Shokurov, Kawamata, Koll\'ar et
al. In dim 4, A was done by 2005 due to Shokurov and...
In this talk, we have two subjects. I. Partial toroidal
compactifications and moduli of PLH. II. The eight enlargements of
Griffiths domain D and the fundamental diagram. For I, we have
Theorem. For a given pair of global monodromy and fan, there...
