Equivalences of families of stacky toric Calabi-Yau hypersurfaces

Charles F. Doran; David Favero; Tyler Kelly

doi:10.1090/proc/14154

Equivalences of families of stacky toric Calabi-Yau hypersurfaces

Charles F. Doran
, David Favero
, Tyler Kelly

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartics in P³, and a birational reduction of Reid’s list to 81 families.

Original language	English
Journal	Proceedings of the American Mathematical Society
DOIs	https://doi.org/10.1090/proc/14154
Publication status	Published - 10 Aug 2018

Bibliographical note

Doran, C. F., Favero, D., & Kelly, T. L. Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces. Proceedings of the American Mathematical Society https://doi.org/10.17863/CAM.23215

Keywords

Calabi-Yau varieties
toric varieties
K3 surfaces
derived equivalences
Picard groups
mirror symmetry

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10.1090/proc/14154Licence: None: All rights reserved

Cite this

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title = "Equivalences of families of stacky toric Calabi-Yau hypersurfaces",

abstract = "Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartics in P3, and a birational reduction of Reid{\textquoteright}s list to 81 families.",

keywords = "Calabi-Yau varieties, toric varieties, K3 surfaces, derived equivalences, Picard groups, mirror symmetry",

author = "Doran, \{Charles F.\} and David Favero and Tyler Kelly",

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AU - Favero, David

AU - Kelly, Tyler

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PY - 2018/8/10

Y1 - 2018/8/10

N2 - Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartics in P3, and a birational reduction of Reid’s list to 81 families.

AB - Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartics in P3, and a birational reduction of Reid’s list to 81 families.

KW - Calabi-Yau varieties

KW - toric varieties

KW - K3 surfaces

KW - derived equivalences

KW - Picard groups

KW - mirror symmetry

UR - https://doi.org/10.17863/CAM.23215

UR - https://www.scopus.com/pages/publications/85055044719

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DO - 10.1090/proc/14154

M3 - Article

SN - 0002-9939

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -

Equivalences of families of stacky toric Calabi-Yau hypersurfaces

Abstract

Bibliographical note

Keywords

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