TL;DR
This paper revisits toric mirror symmetry, providing a new proof for smooth toric stacks by relating the Cox construction to the mirror category, enhancing understanding of the algebraic structures involved.
Contribution
It offers a novel proof of mirror symmetry for smooth toric stacks using the Cox construction and categorical invariants, clarifying the mirror relationship.
Findings
New proof of mirror symmetry for smooth toric stacks
Categorical description of coherent sheaves as invariants in quotient categories
Enhanced understanding of the Cox construction's role in mirror symmetry
Abstract
The Cox construction presents a toric variety as a quotient of affine space by a torus. The category of coherent sheaves on the corresponding stack thus has an evident description as invariants in a quotient of the category of modules over a polynomial ring. Here we give the mirror to this description, and in particular, a clean new proof of mirror symmetry for smooth toric stacks.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Nonlinear Waves and Solitons