Contents Online
Asian Journal of Mathematics
Volume 18 (2014)
Number 2
Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
Pages: 321 – 344
DOI: https://dx.doi.org/10.4310/AJM.2014.v18.n2.a7
Authors
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.
Keywords
walls, Bridgeland stability, polynomial stability, derived category
2010 Mathematics Subject Classification
Primary 14D20. Secondary 14F05, 14J60.
Published 13 May 2014