Hypertoric geometry and Gromov-Witten theory
Yunfeng Jiang, Hsian-Hua Tseng
TL;DR
This paper explores the Gromov-Witten theory of hypertoric Deligne-Mumford stacks, calculating quantum products via representation theory and comparing invariants with Lawrence toric stacks.
Contribution
It provides new calculations of quantum products and establishes a comparison between Gromov-Witten invariants of hypertoric stacks and Lawrence toric stacks.
Findings
Computed small quantum product operators for hypertoric stacks.
Established a relationship between Gromov-Witten invariants of hypertoric and Lawrence toric stacks.
Enhanced understanding of the interplay between hypertoric geometry and Gromov-Witten theory.
Abstract
We study Gromov-Witten theory of hypertoric Deligne-Mumford stacks from two points of view. From the viewpoint of representation theory, we calculate the operator of small quantum product by a divisor, following \cite{BMO}, \cite{MO}, \cite{MS}. From the viewpoint of Lawrence toric geometry, we compare Gromov-Witten invariants of a hypertoric Deligne-Mumford stack with those of its associated Lawrence toric stack.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Advanced Algebra and Geometry