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A Quantum Lefschetz Theorem without Convexity

Wang, Jun
http://rave.ohiolink.edu/etdc/view?acc_num=osu1587420301053309

Abstract Details

2020, Doctor of Philosophy, Ohio State University, Mathematics.
We prove a genus zero Givental-style mirror theorem for all hypersurfaces in proper toric Deligne-Mumford stacks, which provides an explicit slice on Givental’s Lagrangian cone for such targets. This vastly generalizes the previous mirror theorem for certain hypersurfaces in toric Deligne-Mumford stacks, where a technical assumption called convexity is needed. Our proof relies on the quasimap theory and consists of two parts: (1) we compute small I-functions via p-fields; (2) we prove the genus zero quasimap wall-crossing conjecture for the small I-functions.
Hsian-Hua Tseng (Advisor)
Clemens Herb (Committee Member)
Anderson David (Committee Member)
154 p.
Mathematics
Gromov-Witten theory; quantum Lefschetz theorem; convexity; toric stack; quasimap theory; Wall-crossing; root stack; moduli space; mirror theorem

Recommended Citations

Citations

  • Wang, J. (2020). A Quantum Lefschetz Theorem without Convexity [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587420301053309

    APA Style (7th edition)

  • Wang, Jun. A Quantum Lefschetz Theorem without Convexity. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1587420301053309.

    MLA Style (8th edition)

  • Wang, Jun. "A Quantum Lefschetz Theorem without Convexity." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587420301053309

    Chicago Manual of Style (17th edition)

osu1587420301053309
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This open access ETD is published by The Ohio State University and OhioLINK.