Related papers: A note on stable sheaves on Enriques surfaces II
We give a complete description of all classical Enriques surfaces with non-zero global vector fields. In particular we show that there are such surfaces. The obtained result also applies to supersingular Enriques surfaces fulfilling a…
Let $\bar{Y}$ be a normal surface that is the canonical $\mu_2$- or $\alpha_2$-covering of a classical or supersingular Enriques surface in characteristic $2$. We determine all possible configurations of singularities on $\bar{Y}$, and for…
We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.
We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.
We give a proof of the Morrison-Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphisms of degree two.
We give necessary and sufficient criteria for a smooth Enriques surface S in P^r to be scheme-theoretically an intersection of quadrics. Moreover we prove in many cases that, when S contains plane cubic curves, the intersection of the…
We give sufficient conditions for the (semi-)stability of torsion free sheaves on a primitive multiple curve. These conditions are used to prove that some moduli spaces of stable sheaves are not empty. We study mainly the quasi locally free…
Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd…
We investigate exceptional sheaves on the Hirzebruch surface $\mathbb{F}_2$, as the first attempt toward the classification of exceptional objects on weak del Pezzo surfaces.
We give necessary and sufficient conditions for the hull of a coherent sheaf to be coherent.
We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.
We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.
We shall introduce a stability condition for a coherent sheaf associated to an elliptic surface. Then we study the behavior under relative Fourier-Mukai transforms.
We use wall-crossing in the Bridgeland stability manifold to systematically study the birational geometry of the moduli space $M_\sigma(\mathbf{v})$ of $\sigma$-semistable objects of class $\mathbf{v}$ for a generic stability condition…
Making suitable generalizations of known results we prove some general facts about Gaussian maps. The above are then used, in the second part of the article, to give a set of conditions that insure the surjectivity of Gaussian maps for…
We construct moduli stacks of stable sheaves for surfaces fibered over marked nodal curves by using expanded degenerations. These moduli stacks carry a virtual class and therefore give rise to enumerative invariants. In the case of a…
We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived…
We prove existence of reflexive sheaves on singular surfaces and threefolds with prescribed numerical invariants and study their moduli.
We study the flatness of log-pluricanonical sheaves on stable families of surfaces.
In this article, we show that some semi-rigid $\mu$-stable sheaves on a projective K3 surface $X$ with Picard number 1 are stable in the sense of Bridgeland's stability condition. As a consequence of our work, we show that the special set…