Related papers: A note on stable sheaves on Enriques surfaces

We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.

We prove existence of reflexive sheaves on singular surfaces and threefolds with prescribed numerical invariants and study their moduli.

We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. Our formula generalizes Kawai-Yoshioka's formula for stable pairs with…

We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. This improves and completes our previous result joint with Nuer…

We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. We apply the same techniques to give a new simple proof…

We show that when a K3 surface acquires a node, the existence of stable spherical sheaves of certain Chern classes can be obstructed.

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…

Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…

For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of…

The purpose of this note is to give a new proof of Alexeev's boundedness result for stable surfaces which is independent of the base field and to highlight some important consequences of this result.

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 study the flatness of log-pluricanonical sheaves on stable families of surfaces.

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 give an explicit description of the Godeaux surfaces that admit an involution such that the quotient surface is birational to an Enriques surface; these surfaces give a 6-dimensional unirational irreducible subset of the moduli space of…

We shall study the wall crossing behavior of moduli of stable sheaves on an elliptic surface.

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 give a stack-theoretic proof for some results on families of hyperelliptic curves.

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 prove the existence (in characteristic 0) on every polarized (smooth, projective and connected) surface of stable bundles of rank $r\geq 2$, arbitrary first Chern class and large enough $c_2$.

We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.