Related papers: Modular Serre Correspondence via stable pairs

We give a new proof of the following theorem: moduli spaces of stable complexes on a complex projective K3 surface, with primitive Mukai vector and with respect to a generic Bridgeland stability condition, are hyperk\"{a}hler varieties of…

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by…

Let X be a projective irreducible smooth algebraic variety. A "fine moduli space" of sheaves on X is a family F of coherent sheaves on X parametrized by an integral variety M such that : F is flat on M; for all distinct points x, y of M the…

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

The moduli space of holomorphic maps from Riemann surfaces to the Grassmannian is known to have two kinds of compactifications: Kontsevich's stable map compactification and Marian-Oprea-Pandharipande's stable quotient compactification. Over…

The aim of this paper is to prove the existence of large complete subvarieties in moduli spaces of rank two stable sheaves with arbitrary $c_1$ and sufficiently large $c_2$ on algebraic surfaces. Then we study the restriction of these…

We prove that every proper subspace of the moduli space of stable surfaces with fixed volume over an algebraically closed field of characteristic p>5 is projective. As a consequence we also deduce that the same moduli space is projective…

We classify all isomorphisms between moduli stacks of vector bundles of fixed determinant on a smooth complex projective of genus at least 4. It is shown that each isomorphism between two different moduli stacks can be described as a…

The compactification $\overline M_{1,3}$ of the Gieseker moduli space of surfaces of general type with $K_X^2 =1 $ and $\chi(X)=3$ in the moduli space of stable surfaces parametrises so-called stable I-surfaces. We classify all such…

In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2, semi-stable, torsion-free sheaves with fixed odd degree determinant over a very general irreducible nodal curve of genus at least 2. We…

We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a…

Consider an ample and globally generated line bundle $L$ on a smooth projective variety $X$ of dimension $N\geq 2$ over $\mathbb{C}$. Let $D$ be a smooth divisor in the complete linear system of $L$. We construct reflexive sheaves on $X$ by…

Let X be a smooth projective curve of genus g \geq 2 over an algebraically closed field k of characteristic p > 0. Let M_X be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map…

Families of stable curves of genus $\gamma$ over a smooth curve $C$ correspond to morphisms from $C$ to the moduli stack of stable curves $\bar{\cal M}_\gamma$. It is natural to compactify the corresponding moduli problem using stable maps…

We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a…

We describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the three-dimensional projective space whose generic point corresponds to non-locally free sheaves whose singular locus is either…

We study moduli of coherent sheaves of some given degree and positive rank on a curve. We show that there is only one nonempty open condition on families of sheaves that yields a universally closed adequate moduli space, namely, the one…

We prove that the Gieseker moduli space of stable sheaves on a smooth projective threefold $X$ of Picard rank 1 is separated from the moduli space of PT stable objects by a single wall in the space of Bridgeland stability conditions on $X$,…

We show for the moduli space of rank-2 coherent sheaves on an algebraic surface that there exists a 'dual' moduli space. This dual space allows a construction of the first one without using the GIT construction. Furthermore, we obtain a…

Let (X,H) be a polarized, smooth, complex projective surface, and let v be a Chern character on X with positive rank and sufficiently large discriminant. In this paper, we compute the Gieseker wall for v in a slice of the stability manifold…