Exceptional collections for mirrors of invertible polynomials

David Favero; Daniel Kaplan; Tyler Kelly

doi:10.1007/s00209-023-03258-x

Exceptional collections for mirrors of invertible polynomials

David Favero, Daniel Kaplan, Tyler Kelly^*

^*Corresponding author for this work

Mathematics

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Abstract

We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial with its maximal symmetry group. This proves a conjecture of Hirano–Ouchi. In the Gorenstein case, we also prove a stronger version of this conjecture due to Takahashi. Namely, that the full exceptional collection is strong.

Original language	English
Article number	32
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	304
Issue number	2
Early online date	17 May 2023
DOIs	https://doi.org/10.1007/s00209-023-03258-x
Publication status	Published - Jun 2023

Keywords

mirror symmetry
landau-ginzburg models
derived categories
matrix factorizations
geometric invariant theory

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10.1007/s00209-023-03258-xLicence: Creative Commons: Attribution (CC BY)

209_2023_Article_3258.pdfFinal published version, 311 KBLicence: Creative Commons: Attribution (CC BY)

Mirror Constructions:Develop, Unify, Apply
Kelly, T.
Engineering & Physical Science Research Council
1/09/19 → 31/08/22
Project: Research Councils
Bridging Frameworks via Mirror Symmetry
Kelly, T.
Engineering & Physical Science Research Council
1/09/18 → 31/08/19
Project: Research Councils

Cite this

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title = "Exceptional collections for mirrors of invertible polynomials",

abstract = "We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial with its maximal symmetry group. This proves a conjecture of Hirano–Ouchi. In the Gorenstein case, we also prove a stronger version of this conjecture due to Takahashi. Namely, that the full exceptional collection is strong.",

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AU - Favero, David

AU - Kaplan, Daniel

AU - Kelly, Tyler

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N2 - We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial with its maximal symmetry group. This proves a conjecture of Hirano–Ouchi. In the Gorenstein case, we also prove a stronger version of this conjecture due to Takahashi. Namely, that the full exceptional collection is strong.

AB - We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial with its maximal symmetry group. This proves a conjecture of Hirano–Ouchi. In the Gorenstein case, we also prove a stronger version of this conjecture due to Takahashi. Namely, that the full exceptional collection is strong.

KW - mirror symmetry

KW - landau-ginzburg models

KW - derived categories

KW - matrix factorizations

KW - geometric invariant theory

UR - http://link.springer.com/journal/209

U2 - 10.1007/s00209-023-03258-x

DO - 10.1007/s00209-023-03258-x

M3 - Article

SN - 0025-5874

VL - 304

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 2

M1 - 32

ER -

Exceptional collections for mirrors of invertible polynomials

Abstract

Keywords

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Projects

Mirror Constructions:Develop, Unify, Apply

Bridging Frameworks via Mirror Symmetry

Cite this