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 Title: Quantum cohomology of a Hilbert scheme of a Hirzebruch surface Author(s): Fu, Yong Director of Research: Katz, Sheldon Doctoral Committee Chair(s): Nevins, Thomas A. Doctoral Committee Member(s): Katz, Sheldon; Bradlow, Steven B.; Schenck, Henry K. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(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. Issue Date: 2010-08-20 URI: http://hdl.handle.net/2142/16874 Rights Information: Copyright 2010 Yong Fu Date Available in IDEALS: 2010-08-20 Date Deposited: 2010-08
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