Moduli of PT-Semistable Objects I

Abstract

We show boundedness for PT-semistable objects of any Chern classes on a smooth projective three-fold $X$. Then we show that the stack of objects in the heart $\langle \Coh_{\leq 1}(X), \Coh_{\geq 2}(X)[1] \rangle$ satisfies a version of the valuative criterion for completeness. In the remainder of the paper, we give a series of results on how to compute cohomology with respect to this heart.

23 pages

References in corpus (4)

• Curve counting via stable pairs in the derived category
• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• Polynomial Bridgeland stability conditions and the large volume limit
• Limit stable objects on Calabi-Yau 3-folds

Cited by in corpus (10)

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• A mathematical theory of D-string world-sheet instantons, I: Compactness of the stack of $Z$-semistable Fourier-Mukai transforms from a compact family of nodal curves to a projective Calabi-Yau 3-fold
• Stability and Fourier-Mukai transforms on elliptic fibrations
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
• Intrinsic Stabilizer Reduction and Generalized Donaldson-Thomas Invariants
• A relation between higher-rank PT stable objects and quotients of coherent sheaves
• Representing stable complexes on projective spaces