In Lafforgue's proof of the Langlands conjecture for GL(2) over
a functional field, an important step is to compactify the moduli
spaces of Drinfeld's shtukas. In this talk, I will present a new
approach to this problem using the Geometric Invariant...
We start by stating the general form of the Minimal Model
Conjecture and explain the relevance of some recent work of
Bouksom-Demailly-Paun-Peternell. After that we describe the general
picture of the proof of Hacon et al for the general type case.
First we define, for any analytic manifold $X$ of dimension $n$,
locally residual currents; $C^{q,p}$ denotes the sheaf of locally
residual currents of bidegree $(q,p)$. Then, we have a fundamental
resolution of the sheaf of holomorphic $q-$forms $...
This will be an informal working seminar, trying to understand
the recent paper of Birkar, Cascini, Hacon and McKernan on the
finite generation of canonical rings.
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...
