The coherent-constructible correspondence and Fourier-Mukai transforms

Bohan Fang; Chiu Chu Melissa Liu; David Treumann; Eric Zaslow

doi:10.1007/s10114-011-0462-4

The coherent-constructible correspondence and Fourier-Mukai transforms

Bohan Fang^*, Chiu Chu Melissa Liu, David Treumann, Eric Zaslow

^*Corresponding author for this work

Mathematics

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

5 Scopus citations

Abstract

As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝⁿ. In this paper we investigate and reprove some of Kawamata's results from this perspective.

Original language	English (US)
Pages (from-to)	275-308
Number of pages	34
Journal	Acta Mathematica Sinica, English Series
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s10114-011-0462-4
State	Published - Feb 2011

Keywords

Fourier-Mukai transforms
Toric orbifolds
coherent sheaves
constructible sheaves

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1007/s10114-011-0462-4

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abstract = "As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝn. In this paper we investigate and reprove some of Kawamata's results from this perspective.",

keywords = "Fourier-Mukai transforms, Toric orbifolds, coherent sheaves, constructible sheaves",

author = "Bohan Fang and Liu, {Chiu Chu Melissa} and David Treumann and Eric Zaslow",

note = "Funding Information: Received September 7, 2010, accepted October 22, 2010 The work of EZ is supported in part by NSF/DMS-0707064",

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T1 - The coherent-constructible correspondence and Fourier-Mukai transforms

AU - Fang, Bohan

AU - Liu, Chiu Chu Melissa

AU - Treumann, David

AU - Zaslow, Eric

N1 - Funding Information: Received September 7, 2010, accepted October 22, 2010 The work of EZ is supported in part by NSF/DMS-0707064

PY - 2011/2

Y1 - 2011/2

N2 - As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝn. In this paper we investigate and reprove some of Kawamata's results from this perspective.

AB - As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝn. In this paper we investigate and reprove some of Kawamata's results from this perspective.

KW - Fourier-Mukai transforms

KW - Toric orbifolds

KW - coherent sheaves

KW - constructible sheaves

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 2

ER -

The coherent-constructible correspondence and Fourier-Mukai transforms

Abstract

Keywords

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