Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing

Aaron Bertram; Cristian Martinez

doi:10.1093/imrn/rny065

Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing

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

Abstract

We prove that the "Thaddeus flips" of L-twisted sheaves constructed by Matsuki and Wentworth explaining the change of polarization for Gieseker semistable sheaves on a surface can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of one-dimensional Gieseker semistable sheaves on a surface by varying a family of stability conditions.

Original language	English (US)
Pages (from-to)	2007-2033
Number of pages	27
Journal	International Mathematics Research Notices
Volume	2020
Issue number	7
DOIs	https://doi.org/10.1093/imrn/rny065
State	Published - Apr 8 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rny065

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AB - We prove that the "Thaddeus flips" of L-twisted sheaves constructed by Matsuki and Wentworth explaining the change of polarization for Gieseker semistable sheaves on a surface can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of one-dimensional Gieseker semistable sheaves on a surface by varying a family of stability conditions.

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Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing

Abstract

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