Quantum cohomology of a Hilbert scheme of a Hirzebruch surface
Fu, Yong
Loading…
Permalink
https://hdl.handle.net/2142/16874
Description
Title
Quantum cohomology of a Hilbert scheme of a Hirzebruch surface
Author(s)
Fu, Yong
Issue Date
2010-08-20T18:00:31Z
Director of Research (if dissertation) or Advisor (if thesis)
Katz, Sheldon
Doctoral Committee Chair(s)
Nevins, Thomas A.
Committee Member(s)
Katz, Sheldon
Bradlow, Steven B.
Schenck, Henry K.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Gromov-Witten invariants
quantum product
Abstract
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
