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Katz, Sheldon Nevins, Thomas A. Katz, Sheldon Bradlow, Steven B. Schenck, Henry K. Fu, Yong 2010-08-20T18:00:31Z 2010-08-20T18:00:31Z 2010-08-20T18:00:31Z 2010-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-13T17:46:30Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Fu_Yong.pdf: 551273 bytes, checksum: 3842d1e649e799b6f0df3d029e92ba6b (MD5) Made available in DSpace on 2010-08-20T18:00:31Z (GMT). No. of bitstreams: 2 Fu_Yong.pdf: 551273 bytes, checksum: 3842d1e649e799b6f0df3d029e92ba6b (MD5) license.txt: 4055 bytes, checksum: 7b30b936bbf2c2ef1c16fd7dcadcf0ee (MD5) http://hdl.handle.net/2142/16874 en Copyright 2010 Yong Fu Gromov-Witten invariants quantum product Quantum cohomology of a Hilbert scheme of a Hirzebruch surface Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD