Moduli of Bridgeland semistable holomorphic triples

Abstract

We prove that the moduli stack of Bridgeland semistable holomorphic triples over a curve of $g(C)\ge 1$ with a fixed numerical class and phase is an algebraic stack of finite type over $\mathbb{C}$ and admits a proper good moduli space. We prove that this also holds for a class of Bridgeland stability conditions on the category of holomorphic chains ${\mathcal{T}}_{C,n}$. In the process, we construct an explicit geometric realisation of ${\mathcal{T}}_{C,n}$ and prove the open heart property for noetherian hearts in admissible categories of $D^b(X)$, where $X$ is a smooth projective variety over $\mathbb{C}$, whose orthogonal complements are geometric triangulated categories.

arXiv comment30 pages

References in corpus (8)

• Surface group representations in PU(p,q) and Higgs bundles
• Smooth and proper noncommutative schemes and gluing of DG categories
• Hochschild homology and semiorthogonal decompositions
• Existence of moduli spaces for algebraic stacks
• A tour about existence and uniqueness of dg enhancements and lifts
• Stability conditions in families
• Geometric realizations of quiver algebras
• Bridgeland stability conditions on the category of holomorphic triples over curves