Equivalences of families of stacky toric calabi-yau hypersurfaces

Charles F. Doran; David Favero; Tyler L. Kelly

doi:10.1090/proc/14154

Equivalences of families of stacky toric calabi-yau hypersurfaces

Charles F. Doran
, David Favero
, Tyler L. Kelly

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

3 Scopus citations

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 (US)
Pages (from-to)	4633-4647
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	11
DOIs	https://doi.org/10.1090/proc/14154
State	Published - 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
©2018 American Mathematical Society.

Keywords

And phrases
Calabi-yau varieties
Derived equivalences
K3 surfaces
Mirror symmetry
Picard groups
Toric varieties

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10.1090/proc/14154

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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 = "And phrases, Calabi-yau varieties, Derived equivalences, K3 surfaces, Mirror symmetry, Picard groups, Toric varieties",

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year = "2018",

doi = "10.1090/proc/14154",

language = "English (US)",

volume = "146",

pages = "4633--4647",

journal = "Proceedings of the American Mathematical Society",

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TY - JOUR

T1 - Equivalences of families of stacky toric calabi-yau hypersurfaces

AU - Doran, Charles F.

AU - Favero, David

AU - Kelly, Tyler L.

PY - 2018

Y1 - 2018

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 - And phrases

KW - Calabi-yau varieties

KW - Derived equivalences

KW - K3 surfaces

KW - Mirror symmetry

KW - Picard groups

KW - Toric varieties

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

UR - https://www.scopus.com/pages/publications/85055044719#tab=citedBy

U2 - 10.1090/proc/14154

DO - 10.1090/proc/14154

M3 - Article

AN - SCOPUS:85055044719

SN - 0002-9939

VL - 146

SP - 4633

EP - 4647

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Equivalences of families of stacky toric calabi-yau hypersurfaces

Abstract

Bibliographical note

Keywords

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