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Equivariant Moduli Theory on K3 Surfaces

Chen, Yuhang
http://rave.ohiolink.edu/etdc/view?acc_num=osu1658437849046804

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Mathematics.
We study the orbifold Hirzebruch-Riemann-Roch (HRR) theorem for quotient Deligne-Mumford stacks, explore its relation with representation theory of finite groups, and derive an orbifold HRR formula via an orbifold Mukai pairing. As a first application, we use this formula to compute the dimensions of G-equivariant moduli spaces of stable sheaves on a K3 surface X under the action of a finite subgroup G of its symplectic automorphism group. We then apply the orbifold HRR formula to reproduce the number of fixed points on X when G is cyclic without using the Lefschetz fixed point formula. We prove that under some mild conditions, equivariant moduli spaces of stable sheaves on X are irreducible symplectic manifolds deformation equivalent to Hilbert schemes of points on X via a connection between Gieseker and Bridgeland moduli spaces, as well as the derived McKay correspondence. As a corollary, these moduli spaces are also deformation equivalent to equivariant Hilbert schemes of points on X.
Hsian-Hua Tseng (Advisor)
Yunfeng Jiang (Committee Member)
James Cogdell (Committee Member)
David Anderson (Committee Member)
206 p.
Mathematics
Equivariant moduli theory; K3 surfaces; quotient stacks; orbifold Hirzebruch-Riemann-Roch; orbifold Mukai pairing; Bridgeland stability conditions; equivariant Hilbert schemes

Recommended Citations

Citations

  • Chen, Y. (2022). Equivariant Moduli Theory on K3 Surfaces [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1658437849046804

    APA Style (7th edition)

  • Chen, Yuhang. Equivariant Moduli Theory on K3 Surfaces. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1658437849046804.

    MLA Style (8th edition)

  • Chen, Yuhang. "Equivariant Moduli Theory on K3 Surfaces." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1658437849046804

    Chicago Manual of Style (17th edition)

osu1658437849046804
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© 2022, some rights reserved.Creative Commons License Equivariant Moduli Theory on K3 Surfaces by Yuhang Chen is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.