Rank One Bridgeland Stable Moduli Spaces on A Principally Polarized Abelian Surface

Abstract

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to express wall-crossings as Mukai flops and show that the moduli spaces are projective.

17 pages, 3 figures

References in corpus (4)

• Markov convexity and local rigidity of distorted metrics
• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions
• Reider's Theorem and Thaddeus Pairs Revisited

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• A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold
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• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Some moduli spaces of Bridgeland's stability conditions
• On some moduli of complexes on K3 surfaces
• Nef cones of Hilbert schemes of points on surfaces
• Stability conditions and birational geometry of projective surfaces
• Walls and asymptotics for Bridgeland stability conditions on 3-folds
• T-structures on elliptic fibrations
• The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
• Bridgeland's stabilities on abelian surfaces
• Families of elliptic curves in ${\mathbb{P}}^3$ and Bridgeland Stability
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• Nef cones of nested Hilbert schemes of points on surfaces
• MMP Via Wall-crossing for Moduli Spaces of Stable Sheaves on an Enriques surface
• Critical k-Very Ampleness for Abelian Surfaces
• Weight functions, tilts, and stability conditions
• Stability and Fourier-Mukai transforms on elliptic fibrations
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
• Stable sheaves on bielliptic surfaces: from the classical to the modern
• Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points
• On the birational geometry of Hilbert schemes of points and Severi divisors