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April 2014 Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
Jason Lo, Zhenbo Qin
Asian J. Math. 18(2): 321-344 (April 2014).

Abstract

For the derived category of bounded complexes of sheaves on a smooth projective surface, Bridgeland and Arcara-Bertram constructed Bridgeland stability conditions $(Z_m , \mathcal{P}_m)$ parametrized by $m \in (0, {+\infty})$. In this paper, we show that the set of mini-walls in $(0, {+\infty})$ of a fixed numerical type is locally finite. In addition, we strengthen a result of Bayer by proving that the moduli of polynomial Bridgeland semistable objects of a fixed numerical type coincides with the moduli of $(Z_m , \mathcal{P}_m)$-semistable objects whenever $m$ is larger than a universal constant depending only on the numerical type. We further identify the moduli of polynomial Bridgeland semistable objects with the Gieseker/Simpson moduli spaces and the Uhlenbeck compactification spaces.

Citation

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Jason Lo. Zhenbo Qin. "Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces." Asian J. Math. 18 (2) 321 - 344, April 2014.

Information

Published: April 2014
First available in Project Euclid: 27 August 2014

zbMATH: 1315.14019
MathSciNet: MR3217639

Subjects:
Primary: 14D20
Secondary: 14F05 , 14J60

Keywords: Bridgeland stability , derived category , polynomial stability , walls

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 2 • April 2014
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