Related papers: 2-Gorenstein stable surfaces with $K_X^2 = 1$ and …

We give infinite series of groups Gamma and of compact complex surfaces of general type S with fundamental group Gamma such that 1) Any surface S' with the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S. 2) The…

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

We give many examples in which there exist infinitely many divisorial conditions on the moduli space of polarized K3 surfaces $(S,H)$ of degree $H^2=2g-2$, $g \geq 3$, and Picard number $rk N(S)=\rho(S)=2$ such that for a general K3 surface…

We compute Betti numbers of the moduli spaces of arbitrary rank stable sheaves on ruled surfaces. Our result generalizes the formula of Goettsche for rank one sheaves and the formula of Yoshioka for rank two sheaves. It also confirms the…

A stable pair on a projective variety consists of a sheaf and a global section subject to stability conditions parameterized by rational polynomials. We will show that for a smooth projective threefold and a class of a rank 2 sheaf, there…

We consider two K3 surfaces defined over an arbitrary field, together with a smooth proper moduli space of stable sheaves on each. When the moduli spaces have the same dimension, we prove that if the \'etale cohomology groups (with Q_ell…

We classify Gorenstein stable numerical Godeaux surfaces with worse than canonical singularities and compute their fundamental groups.

Let $X$ be a K3 surface with Picard group $\mathrm{Pic}(X)\cong\mathbb{Z} H$ such that $H^2=2n$. Let $M_{H}(\mathbf{v})$ be the moduli space of Gieseker semistable sheaves on $X$ with Mukai vector $\mathbf{v}$. We say that $\mathbf{v}$…

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and…

A smooth algebraic surface $S$ is said to be \emph{isogenous to a product of unmixed type} if there exist two smooth curves $C, F$ and a finite group $G$, acting faithfully on both $C$ and $F$ and freely on their product, so that $S=(C…

We construct a new family of simply connected minimal complex surfaces with $p_g=1$, $q=0$, and $K^2=8$ using a $\mathbb{Q}$-Gorenstein smoothing theory.

In this paper, we study the Gieseker moduli space $\mathcal{M}_{1,1}^{4,3}$ of minimal surfaces with $p_g=q=1, K^2=4$ and genus 3 Albanese fibration. Under the assumption that direct image of the canonical sheaf under the Albanese map is…

Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of…

We prove in one go that each of the 4 families of Burniat surfaces with K^2 = 6,5,4, is a connected component of the moduli space of surfaces of general type. We prove also the rationality of each component. In the nodal case (one of the…

Stable surfaces and their log analogues are the type of varieties naturally occuring as boundary points in moduli spaces. We extend classical results of Kodaira and Bombieri to this more general setting: if $(X,\Delta)$ is a stable log…

Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and…

We study the moduli space of congruence classes of isometric surfaces with the same mean curvature in 4-dimensional space forms. Having the same mean curvature means that there exists a parallel vector bundle isometry between the normal…

We give a complete classification of complex Q-homology projective planes with isolated rational double point singularities and numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all…

We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…

The aim of this article is to classify the pairs (S, G), where S is a smooth minimal surface of general type with p_g=0 and K^2=7, G is a subgroup of the automorphism group of S and G is isomorphic to the group $\mathbb{Z}_2^2$. The Inoue…