Special Year 2006-07: Algebraic Geometry

I will give an introduction to spaces of jets of algebraic varieties, explining their relevance for birational geometry. In particular, I will explain why these spaces are useful in the study of singularities.

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 will discuss the ideas of the proof of the finite generation theorem, by looking at several special cases.

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.