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Quasimap Theories for GIT Stack Bundle

Supekar, Shidhesh
http://rave.ohiolink.edu/etdc/view?acc_num=osu1688031234907419

Abstract Details

2023, Doctor of Philosophy, Ohio State University, Mathematics.
In this dissertation we develop $\epsilon$-quasimap theories when the target space is a GIT stack bundle over a smooth projective space and prove wall-crossing formula as $\epsilon$ changes. In chapter [2], we define GIT stack bundle and its presentation. In chapter [3], we define a moduli stack parametrizing quasimaps to GIT stack bundle and show that under certain stability conditions we get a collection of proper Deligne--Mumford stacks indexed by $\epsilon\in\Q_{>0}$. We then show that the integral over the virtual fundamental class of these stacks changes across certain $\epsilon$ in the form of wall-crossing formula. To show that, we define a master space and prove that it is proper and a DM stack in chapter [4]. In chapter [5], we define a $\C^*$-action on this master space such that its fixed loci includes adjacent $\epsilon$-quasimap stacks chambers. Then the wall-crossing formula is given by a simple application of localization which is done in chapter [6]. In the final chapter of the dissertation, we give a formula relating the I-function of GIT scheme bundle to I-function of toric scheme bundle in the form of abelian/nonabelian correspondence.
Hsian-Hua Tseng (Advisor)
98 p.
Mathematics

Recommended Citations

Citations

  • Supekar, S. (2023). Quasimap Theories for GIT Stack Bundle [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1688031234907419

    APA Style (7th edition)

  • Supekar, Shidhesh. Quasimap Theories for GIT Stack Bundle. 2023. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1688031234907419.

    MLA Style (8th edition)

  • Supekar, Shidhesh. "Quasimap Theories for GIT Stack Bundle." Doctoral dissertation, Ohio State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=osu1688031234907419

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.