Related papers: Moduli spaces on Kuznetsov components are Irreduci…

K3 surfaces with non-symplectic involution are classified by open sets of seventy-five arithmetic quotients of type IV. We prove that those moduli spaces are rational except two classical cases.

In this paper, we study relations between automorphism groups of cubic fourfolds and Kuznetsov components. Firstly, we characterize automorphism groups of cubic fourfolds as subgroups of autoequivalence groups of Kuznetsov components using…

In this paper I consider a quintic surface in $\pp^3$, general in the sense of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which are $\mu$-stable with respect to the hyperplane section and have $c_1 = K$, the…

In this paper we investigate the asymptotic growth of the number of irreducible and connected components of the moduli space of surfaces of general type corresponding to certain families of surfaces isogenous to a higher product with group…

This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension…

We define a moduli space of stable regular singular parabolic connections of spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we…

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…

We show that for an orientable non-spin manifold with fundamental group $\mathbb{Z}_2$ and universal cover $S^2\times S^3,$ the moduli space of metrics of nonnegative sectional curvature has infinitely many path components. The…

We describe new explicit examples of moduli spaces of Bridgeland semistable objects on surfaces, parametrizing objects whose numerical class agrees with the class of a point. This follows ideas of Tramel and Xia, using stability conditions…

As their smooth analogue the irreducible symplectic varieties appear as elementary bricks in the generalizations of the Bogomolov decomposition theorem (arXiv:math/0402243, arXiv:2012.00441). Let $S$ be a K3 surface; generalizing the Fujiki…

A torsion-free sheaf $E$ on a projective variety $X$ is called quasi-trivial if $E^{\vee\vee}=\mathcal{O}_{X}^{\oplus r}$. While such sheaves are always $\mu$-semistable, they may not be semistable. We study the Gieseker--Maruyama moduli…

We prove that, for a natural class of Bridgeland stability conditions on $\mathbb{P}^1\times\mathbb{P}^1$ and the blow-up of $\mathbb{P}^2$ at a point, the moduli spaces of Bridgeland semistable objects are projective. Our technique is to…

Let X be a K3 surface and M a smooth and projective moduli space of stable sheaves on X of Mukai vector v. A universal sheaf U over X x M induces an integral transform F from the derived category D(X) of coherent sheaves on X to that on M.…

We construct the moduli space of cubic surfaces which do not admit a Sylvester form as an arithmetic quotient, and determine the graded ring of modular forms of even weights.

Given a linear category over a finite field such that the moduli space of its objects is a smooth Artin stack (and some additional conditions) we give formulas for an exponential sum over the set of absolutely indecomposable objects and a…

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with…

We prove that minimal instanton bundles on a Fano threefold $X$ of Picard rank one and index two are semistable objects in the Kuznetsov component $\mathsf{Ku}(X)$, with respect to the stability conditions constructed by Bayer, Lahoz,…

Let $M_c=M(2,0,c)$ be the moduli space of O(1)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0$ and $c_2=c$ on a K3 surface $X$ where O(1) is a generic ample line bundle on $X$. When $c=2n\geq4$ is even, $M_c$ is a singular…

The Hessian of a general cubic surface is a nodal quartic surface, hence its desingularisation is a K3 surface. We determine the transcendental lattice of the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt points…

Let $\mathcal Q_D$ be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order $\mathcal O$ in an indefinite quaternion algebra of…