Related papers: A note on stable sheaves on Enriques surfaces

In this paper, we study the Abreu equation on toric surfaces. In particular, we prove the existence of the positive extremal metric when relative $K$-stability is assumed.

In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier Stokes equations. We then recall classical physical instability results, and give a short educational…

We give an explicit construction and clasification of some very special sort of Enriques surfaces in characteristic two. This proves the existence of some of the surfaces that were called ``extra-special'' by Cossec and Dolgachev in their…

We introduce a conjecture on Virasoro constraints for the moduli space of stable sheaves on a smooth projective surface. These generalise the Virasoro constraints on the Hilbert scheme of a surface found by Moreira (arXiv:2008.13746) and…

Recently, Nunge studied Eulerian polynomials on segmented permutations, namely \emph{generalized Eulerian polynomials}, and further asked whether their coefficients form unimodal sequences. In this paper, we prove the stability of the…

We consider the class of singular double coverings $X \to \PP^3$ ramified in the degeneration locus $D$ of a family of 2-dimensional quadrics. These are precisely the quartic double solids constructed by Artin and Mumford as examples of…

In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural…

We prove some extensions of Andrews inequality.

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.

This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we…

We show that the moduli spaces of stable sheaves on projective schemes admit certain non-commutative structures, which we call quasi NC structures, generalizing Kapranov's NC structures. The completion of our quasi NC structure at a closed…

We prove that the limit hypersurfaces of converging curvature flows are stable, if the initial velocity has a weak sign, and give a survey of the existence and regularity results.

We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi-Yau threefold. For this purpose we prove the existence of certain stable vector bundle…

In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0$, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when…

We simplify the usual statement of the Torelli theorem for complex Enriques surfaces, by means of a lattice-theoretic trick. This allows easy proofs of several known results, which previously required intricate arithmetic arguments. The…

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes.

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…

In this paper, we prove the stability of shear flows of Prandtl type as $ \big(U(y/\sqrt{\nu}),0\big)$ for the steady Navier-Stokes equations under a natural spectral assumption on the linearized NS operator. We develop a direct energy…

We study the moduli space of Gieseker semi-stable sheaves on the complex projective plane supported on sextic curves and having Euler characteristic one. We determine locally free resolutions of length one for all such sheaves. We decompose…