Related papers: Moduli of Bridgeland semistable holomorphic triple…

We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. This can be viewed as a `universal phase diagram' for…

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's…

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and…

We define a ring of motivic classes of stacks suitable for symmetric powers in finite characteristic. Let $X$ be a smooth projective curve over a field of arbitrary characteristic. We calculate the motivic classes of the moduli stacks of…

Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show…

We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank 3 and coprime degree on a smooth projective curve. Our approach involves identifying criteria to lift identities in (a…

In this work more questions arise than answers given, for which of course we do not apologize. The core of this paper is concerned with the construction of a ``constant'' t-structure on the bounded derived category of coherent sheaves…

In this paper we construct the moduli of semistable principal bundles with structure group a semisimple group, over nonsingular curves in positive characteristic, with good bounds on the prime.

We introduce multi-uniformized stacks as a generalization of the Abramovich--Hassett construction of uniformized twisted varieties. We prove an equivalence between the category of multi $\mathbb{Q}$-line bundles satisfying an analogue of…

In the present thesis we study the geometry of the moduli spaces of Bradlow-Higgs triples on a smooth projective curve $C$. $(E,\varphi, s)$ is a Bradlow-Higgs triple if $(E,\varphi)$ is a Higgs bundle and $s$ is a non-zero global section…

Let $\pi : X = \mathbb{P}_C(E) \longrightarrow C$ be a ruled surface over an algebraically closed field $k$ of characteristic 0, with a fixed polarization $L$ on $X$. In this paper, we show that pullback of a (semi)stable Higgs bundle on…

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a…

Let $X$ be a non-singular projective curve of genus $g\ge2$ over an algebraically closed field of characteristic zero. Let $\mo$ denote the moduli space of stable bundles of rank $n$ and degree $d$ on $X$ and $\wn $ the Brill-Noether loci…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

In this paper, we prove BG-type inequality conjecture for threefolds in the title. In particular, there exist Bridgeland stability conditions on these threefolds.

In arXiv:2407.11958, a moduli stack parametrizing $I$--indexed diagrams of Higgs bundles over a base stack $X$ was constructed for any finite simplicial set $I$, inspiring speculations about extending the non-Abelian Hodge correspondence to…

Fix a polarised Calabi-Yau threefold $(X,H)$. We reduce a version of the Bayer-Macr\`i-Toda conjecture for $(X,H)$, which ensures the existence of Bridgeland stability conditions on $X$, to verifying a Brill-Noether-type inequality for…

For $g,n\geq 0$ a 3-dimensional Calabi-Yau $A_\infty$-category $\mathcal C_{g,n}$ is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Stab}(\mathcal C_{g,n})$, is a moduli space of quadratic…

We consider a class of tautological top intersection products on the moduli space of stable pairs consisting of semistable vector bundles together with N sections on a smooth complex projective curve C. We show that when N is large, these…

This article studies moduli spaces of Bridgeland semistable objects in the Kuznetsov component of a cubic fourfold that don't admit a symplectic resolution, i.e., moduli spaces of objects with non-primitve Mukai vector v=mv_0 that is not of…