Quantum cohomology of a Hilbert scheme of a Hirzebruch surface

In this thesis, we first use the {\mathbb C^*}²-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some two-pointed Gromov-Witten invariants via virtual localization, then making intensive use of the associativity law satisfied by quantum product, calculate other Gromov-Witten invariants sufficient for us to determine the structure of quantum cohomology ring of the Hilbert scheme. The novel point of this work is that we manage to avoid families of invariant curves with the freedom of choosing cycles to apply virtual localization method.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Fu, Yong

Contributors dc:contributor

• Katz, Sheldon
• Nevins, Thomas A.
• Bradlow, Steven B.
• Schenck, Henry K.

• Gromov-Witten invariants
• quantum product

Statement dc:rights

• Copyright 2010 Yong Fu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16874

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16874