Quantum cohomology of a Hilbert scheme of a Hirzebruch surface
by Fu, Yong, Ph.D., UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN, 2010, 143 pages; 3452167

Abstract:

In this thesis, we first use a [special characters omitted]-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 the virtual localization method.

 
AdvisersThomas Nevins; Sheldon Katz
SchoolUNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
SourceDAI/B 72-06, p. , May 2011
Source TypeDissertation
SubjectsMathematics; Quantum physics; Theoretical mathematics
Publication Number3452167
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