May 7, 2002

Ilya Tyomkin

Title: Singular curves on algebraic surfaces

Abstract:

We will consider the following question: Given an algebraic pojective surface $S$, linear system $\vert D\vert\in Pic(S)$ and topological types of isolated singularities $S_1,\ldots, S_r$, does there exist an irreducible reduced curve $C\in \vert D\vert$ having exactly $r$ singular points of types $S_1,\ldots, S_r$?

In our talk we will give a sufficient numerical condition (on $\vert D\vert$, $\mu(S_i)$) for existence of such a curve and we will consider some examples of surfaces where this condition become easily checkable. (Joint work with Thomas Keilen from Kaiserslautern)