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Thesis.pdf (692.32 KB)
ETD Abstract Container
Abstract Header
A Mirror Theorem for Toric Stack Bundles
Author Info
You, Fenglong
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1494255385887568
Abstract Details
Year and Degree
2017, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
This thesis is based on joint work with Yunfeng Jiang and Hsian-Hua Tseng \cite {JTY}. This thesis investigates the orbifold Gromov-Witten theory of toric stack bundles and proves a mirror symmetry theorem for toric stack bundles. We study Givental's Lagrangian cone for the quantum orbifold cohomology of toric stack bundles. Using Gromov-Witten invariants of the base and combinatorics of the toric stack fibers, we construct an explicit slice of the Lagrangian cone defined by the genus $0$ Gromov-Witten theory of a toric stack bundle. The slice that we constructed is call the $I$-function for toric stack bundles. We prove a characterization theorem for the Lagrangian cone of toric stack bundles via recursion relation. Then we prove that the $I$-function for toric stack bundles satisfies the conditions for characterization. The main technique that is used in the proof is virtual localization.
Committee
Hsian-Hua Tseng (Advisor)
David Anderson (Committee Member)
Angélica Cueto (Committee Member)
Pages
109 p.
Subject Headings
Mathematics
Keywords
Orbifold Gromov Witten theory of toric stack bundles
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Citations
You, F. (2017).
A Mirror Theorem for Toric Stack Bundles
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1494255385887568
APA Style (7th edition)
You, Fenglong.
A Mirror Theorem for Toric Stack Bundles.
2017. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1494255385887568.
MLA Style (8th edition)
You, Fenglong. "A Mirror Theorem for Toric Stack Bundles." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1494255385887568
Chicago Manual of Style (17th edition)
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Document number:
osu1494255385887568
Download Count:
546
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.