Back to Algebraic Geometry Seminar: Spring 2014
Algebraic Geometry Seminar
Date: Tuesday, Feb 25, 2014
Time: 3:30PM - 4:30PM
Location: LCB 215
Qile Chen
Columbia University
Title |
A^1-curves on quasi-projective varieties |
Abstract |
The theory of stable log maps was developed recently for studying the degeneration of Gromov-Witten invariants. In this talk, I will introduce another important aspect of stable log maps as a useful tool for investigating A^1-curves on quasi-projective varieties, which are the analogue of rational curves on proper varieties. At least two interesting applications of A^1-curves will be introduced in this talk. For classical birational geometry, the A^1-curves can be used to produce very free rational curves on Fano complete intersections in projective spaces. On the arithmetic side, A^1-connectedness gives a general frame work for the existence of integral points over function field of curves. This is joint work with Yi Zhu. |
Algebraic Geometry