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

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.

arXiv comment26 pages

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• Gluing stability conditions

Cited by in corpus (6)

• Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces
• A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• On some moduli of complexes on K3 surfaces
• Some examples of tilt-stable objects on threefolds
• Representing stable complexes on projective spaces