Intrinsic mirrors for minimal adjoint orbits and categories of singularities

Fuente: arXiv
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1. Verfasser: Gasparim, Elizabeth
Format: Preprint
Veröffentlicht: 2021
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author Gasparim, Elizabeth
author_facet Gasparim, Elizabeth
contents I discuss mirrors of Landau-Ginzburg models formed by a minimal semisimple adjoint orbit of $\mathfrak{sl}(n)$ together with a potential obtained via the Cartan-Killing form. I show that the Landau-Ginzburg models produced by the Gross-Siebert recipe give precisely the objects of the desired mirrors. It is known that Landau-Ginzburg model $LG(2)$ over the semisimple adjoint orbit of $\mathfrak{sl}(2)$ does not have projective mirrors. I prove Homological Mirror Symmetry for $LG(2)$ by constructing a Landau-Ginzburg mirror and showing that its Orlov category of singularities is equivalent to $Fuk(LG(2))$.
format Preprint
id arxiv_https___arxiv_org_abs_2108_02471
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Intrinsic mirrors for minimal adjoint orbits and categories of singularities
Gasparim, Elizabeth
Algebraic Geometry
Symplectic Geometry
I discuss mirrors of Landau-Ginzburg models formed by a minimal semisimple adjoint orbit of $\mathfrak{sl}(n)$ together with a potential obtained via the Cartan-Killing form. I show that the Landau-Ginzburg models produced by the Gross-Siebert recipe give precisely the objects of the desired mirrors. It is known that Landau-Ginzburg model $LG(2)$ over the semisimple adjoint orbit of $\mathfrak{sl}(2)$ does not have projective mirrors. I prove Homological Mirror Symmetry for $LG(2)$ by constructing a Landau-Ginzburg mirror and showing that its Orlov category of singularities is equivalent to $Fuk(LG(2))$.
title Intrinsic mirrors for minimal adjoint orbits and categories of singularities
topic Algebraic Geometry
Symplectic Geometry
url https://arxiv.org/abs/2108.02471