Qile Chen : Compactifying the space of relative stable maps using logarithmic structures

Posted by , part of the Algebraic Geometry Seminar.

At

Jan. 19, 2011, 4 p.m.

In

SEO 1227

Abstract

For the purpose of computing Gromov-Witten invariants, the compactification of the space of relative stable maps with respect to a smooth divisor were introduced and studied using expanded degeneration during the past decade. Starting from the backgrounds and basic definitions, I will introduce a new way of compactification using logarithmic structures in the sense of Kato-Fontaine-Illusie. In particular, this covers many interesting cases, such as the target variety with a simple normal crossings divisor, or a simple normal crossings degeneration of a variety with simple normal crossings singularities. This is in part joint work with Dan Abramovich.