Special Year 2006-07: Algebraic Geometry - Seminar

Consider an arrangement of nonsingular subvarieties in a nonsingular algebraic variety. We define a compactification of the complement by replacing these subvarieties with a normal crossing divisor. This compactification is obtained by a sequence of...

Let $X\subset \P^N$ be a projective submanifold of dimension $n$ in the complex projective space $\P^N$. Let $U$ be a domain in the parameter space $T$ of complete intersections of codimension $m$ and of a given bidegree $(d_1,\dots,d_m)$ in $\P^N$...

The talk is based on the joint work with Boris Doubrov. First we will describe a new rather effective procedure of symplectification for the problem of local equivalence of nonholonomic vector distributions. The starting point of this procedure is...

We will finish the sketch of the proof of existence of a geometrically meaningful compactification of the moduli space of canonically polarized smooth varieties.

Characteristic classes of Flat bundles on smooth algebraic varieties are defined in various cohomology theories. We consider the de Rham cohomology, the Deligne cohomology and the rational Chow groups and study the classes. We focus on the special...

In 1991, Witten proposed a famous conjecture (solved by Kontsevich) related the intersection theory of Deligne-Mumford moduli space to KDV-integrable hierearchy. To generalize his conjecture, Witten proposed a remarkable PDE based any...

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.