Quantum cohomology of a Hilbert scheme of a Hirzebruch surface

Gromov-Witten invariants;quantum product

Fu, Yong

关键词: Gromov-Witten invariants;    quantum product;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16874/Fu_Yong.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.