Open Collections

Tropicalizing cycle classes and a correspondence theorem for descendant invariants

Banff International Research Station for Mathematical Innovation and Discovery

Intersection theory is an extremely useful tool both in algebraic and tropical enumerative geometry. It can also be used to obtain algebraic/tropical correspondence theorems. The idea is to apply the tropicalization procedure to appropriate intersection products on suitable algebraic moduli spaces, thus obtaining the analogous tropical intersection products on the analogous tropical moduli spaces. For this to work in general, we need to be able to tropicalize cycle classes. I will present a suitable definition of tropical rational equivalence on extended cone complexes making this possible. As an application we obtain a correspondence theorem for genus 0 logarithmic descendant Gromov-Witten invariants of toric varieties.

Mathematics; Algebraic geometry; Combinatorics

video/mp4

Author affiliation: TU Kaiserslautern

2016-11-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59624

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/