Related papers: Stable vector bundles on algebraic surfaces

The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows…

We study the non-emptyness of moduli of stable sheaves on an elliptic ruled surface with a nef. anticanonical bundle.

Let $X$ be a projective K3 surfaces. In two examples where there exists a fine moduli space $M$ of stable vector bundles on $X$, isomorphic to a Hilbert scheme of points, we prove that the universal family $\mathcal{E}$ on $X\times M$ can…

Let $C$ be a smooth, projective, geometrically irreducible curve defined over $\mathbb{R}$ such that $C(\mathbb{R}) = \emptyset$. Let $r>0$ and $d$ be integers which are coprime. Let $L$ be a line bundle on $C$ which corresponds to an…

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli…

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.

Let $X$ be a smooth, irreducible, projective algebraic surface, and let $\alpha \in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $\alpha$-stable coherent…

We study Brauer-Severi surface bundles over smooth projective varieties via root stacks, with a view towards applications to failure of stable rationality.

We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families…

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

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.

Let $S$ be a ruled surface inside a smooth threefold $W$ and let $E$ be a vector bundle on a formal neighborhood of $S.$ We find minimal conditions under which the local moduli space of $E$ is finite dimensional and smooth. Moreover, we…

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the…

Let X be a ruled surface over a nonsingular curve C of genus $g\geq0$. Let $M_H:=M_{X,H}(2;c_1,c_2)$ be the moduli space of H-stable rank 2 vector bundles E on X with fixed Chern classes $c_i:=c_i(E)$ for $i=1,2$. The main goal of this…

We give an explicit groupoid presentation of certain stacks of vector bundles on formal neighborhoods of rational curves inside algebraic surfaces. The presentation involves a M\"obius type action of an automorphism group on a space of…

We determine all of lines in the moduli space $M$ of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…

This is a survey paper: we discuss certain recent results, with some improvements. It will appear in the S. Cruz proceedings.

This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is…

Let $\pi: X \longrightarrow C$ be a fibration with reduced fibers over a curve $C$ and consider a polarization $H$ on the surface $X$. Let $E$ be a stable vector bundle of rank $2$ on $C$. We prove that the pullback $\pi^*E$ is a $H-$stable…