On some moduli of complexes on K3 surfaces

Abstract

We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces. On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a moduli stack of slope semistable locally free sheaves on the Fourier-Mukai partner $\hat{X}$. This yields a morphism from the stack of Bridgeland semistable objects to a projective scheme, which induces an injection on closed points. It also allows us to extend a theorem of Bruzzo-Maciocia on Hilbert schemes to a statement on moduli of complexes.

8 pages

References in corpus (7)

• Rank One Bridgeland Stable Moduli Spaces on A Principally Polarized Abelian Surface
• Good moduli spaces for Artin stacks
• Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions
• Some moduli spaces of Bridgeland's stability conditions
• Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
• Postnikov-Stability versus Semistability of Sheaves
• Derived and abelian equivalence of K3 surfaces

Cited by in corpus (5)

• Birational Geometry of Singular Moduli Spaces of O'Grady Type
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• MMP Via Wall-crossing for Moduli Spaces of Stable Sheaves on an Enriques surface
• Stability and Fourier-Mukai transforms on elliptic fibrations
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations