Asian Journal of Mathematics

Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces

Jason Lo and Zhenbo Qin

Full-text: Open access

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.

Article information

Source
Asian J. Math., Volume 18, Number 2 (2014), 321-344.

Dates
First available in Project Euclid: 27 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1409168527

Mathematical Reviews number (MathSciNet)
MR3217639

Zentralblatt MATH identifier
1315.14019

Subjects
Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]

Keywords
Walls Bridgeland stability polynomial stability derived category

Citation

Lo, Jason; Qin, Zhenbo. Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces. Asian J. Math. 18 (2014), no. 2, 321--344. https://projecteuclid.org/euclid.ajm/1409168527


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