Bow varieties: Stable envelopes and their 3d mirror symmetry

Fuente: arXiv
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Main Authors: Botta, Tommaso Maria, Rimanyi, Richard
Format: Preprint
Published: 2023
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author Botta, Tommaso Maria
Rimanyi, Richard
author_facet Botta, Tommaso Maria
Rimanyi, Richard
contents In this paper we study the elliptic characteristic classes known as ''stable envelopes'', which were introduced by M. Aganagic and A. Okounkov. We prove that for a rich class of holomorphic symplectic varieties$\unicode{x2013}$called Cherkis bow varieties$\unicode{x2013}$their elliptic stable envelopes exhibit a duality property inspired by mirror symmetry in $d=3$, $\mathcal N=4$ quantum field theories. A crucial step of our proof involves the process of ''resolving'' large charge branes into multiple smaller charge branes. This phenomenon turns out to be the geometric counterpart of the algebraic fusion procedure. Along the way we discover various new features in the geometry of bow varieties.
format Preprint
id arxiv_https___arxiv_org_abs_2308_07300
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Bow varieties: Stable envelopes and their 3d mirror symmetry
Botta, Tommaso Maria
Rimanyi, Richard
Algebraic Geometry
Mathematical Physics
Quantum Algebra
Representation Theory
55N34, 81T30, 14J33, 20G42, 14C17
In this paper we study the elliptic characteristic classes known as ''stable envelopes'', which were introduced by M. Aganagic and A. Okounkov. We prove that for a rich class of holomorphic symplectic varieties$\unicode{x2013}$called Cherkis bow varieties$\unicode{x2013}$their elliptic stable envelopes exhibit a duality property inspired by mirror symmetry in $d=3$, $\mathcal N=4$ quantum field theories. A crucial step of our proof involves the process of ''resolving'' large charge branes into multiple smaller charge branes. This phenomenon turns out to be the geometric counterpart of the algebraic fusion procedure. Along the way we discover various new features in the geometry of bow varieties.
title Bow varieties: Stable envelopes and their 3d mirror symmetry
topic Algebraic Geometry
Mathematical Physics
Quantum Algebra
Representation Theory
55N34, 81T30, 14J33, 20G42, 14C17
url https://arxiv.org/abs/2308.07300