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Shah, A - Operational and quantum K-theory of toric varieties.pdf (990.33 KB)
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Abstract Header
Operational and quantum K-theory of toric varieties
Author Info
Shah, Aniket M
ORCID® Identifier
http://orcid.org/0000-0002-4150-6863
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu161970007408212
Abstract Details
Year and Degree
2021, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
This thesis contains two different projects on toric geometry. The first project describes the operational K-theory introduced by D. Anderson and S. Payne in [3] for toric varieties, via the introduction of a ring of Grothendieck weights. We prove several properties of Grothendieck weights, which combinatorially characterize them in low dimensions. The second project introduces generalized Rogers-Szego polynomials, which depend on the data of a smooth lattice polytope P. For P an interval these specialize to the polynomials studied in [39]. We prove a q-series identity for these functions involving certain q-hypergeometric functions introduced in [25] and separately in [32]. The identity is a q-deformation of the well-known identity of Brion [9] in Ehrhart theory, and is proved via equivariant K-theory on quasimap spaces. We finish by proving some combinatorial properties of generalized Rogers-Szego polynomials.
Committee
David Anderson (Advisor)
Hsian-Hua Tseng (Committee Member)
Maria Angelica Cueto (Committee Member)
Pages
81 p.
Subject Headings
Mathematics
Keywords
algebraic geometry, K-theory, polyhedra, combinatorics, q-series, toric varieties, quantum K-theory, lattice points
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Citations
Shah, A. M. (2021).
Operational and quantum K-theory of toric varieties
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu161970007408212
APA Style (7th edition)
Shah, Aniket.
Operational and quantum K-theory of toric varieties.
2021. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu161970007408212.
MLA Style (8th edition)
Shah, Aniket. "Operational and quantum K-theory of toric varieties." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu161970007408212
Chicago Manual of Style (17th edition)
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Document number:
osu161970007408212
Download Count:
180
Copyright Info
© 2021, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.