Related papers: On Weddle Surfaces And Their Moduli

We give examples of stable rank 2 vector bundles on principally polarized abelian threefolds, and study their deformations. The starting point is the Serre construction, which gives a source of examples, and which we rephrase in terms of…

Given a smooth genus two curve $C$, the moduli space SU$_C(3)$ of rank three semi-stable vector bundles on $C$ with trivial determinant is a double cover in $\mathbb{P}^8$ branched over a sextic hypersurface, whose projective dual is the…

We analyze the moduli space of non-flat homogeneous affine connections on surfaces. For Type $\mathcal{A}$ surfaces, we write down complete sets of invariants that determine the local isomorphism type depending on the rank of the Ricci…

Fujita's second theorem for K\"ahler fibre spaces over a curve asserts that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. We focus on our…

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…

We prove the modularity of a positive proportion of abelian surfaces over $\mathbf{Q}$. More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and are $3$-distinguished, subject to some assumptions on the…

We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank 2, which appears in the definition of noncommutative…

There is a canonical identification, due to the author, of a convex real projective structure on an orientable surface of genus g and a pair consisting of a conformal structure together with a holomorphic cubic differential on the surface.…

The Hessian of a general cubic surface is a nodal quartic surface, hence its desingularisation is a K3 surface. We determine the transcendental lattice of the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt points…

For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that the space of sections of certain theta bundle on moduli of bundles of rank r and level k is naturally dual to a similar space of sections of…

We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the…

We review a proof of the well know result stating that moduli spaces of stable sheaves with fixed Chern character on a polarized $K3$ surface are deformations of a hyperk\"ahler variety of Type $K3^{[n]}$ (if a suitable numerical hypothesis…

This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves,…

In the first part of this paper we provide a survey of some fundamental results about moduli spaces of framed sheaves on smooth projective surfaces. In particular, we outline a result by Bruzzo and Markushevich, and discuss a few…

We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if $V$ is any stable…

The Desale-Ramanan Theorem is an isomorphism between the moduli space of rank two vector bundles over complex hyperelliptic curve and the variety of linear subspaces in an intersection of two quadrics. We prove a real version of this…

The main result of this paper is a characterization of the abelian varieties $B/K$ defined over Galois number fields with the property that the zeta function $L(B/K;s)$ is equivalent to the product of zeta functions of non-CM newforms for…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

Let ${\mathcal B}_g(r)$ be the moduli space of triples of the form $(X,\, K^{1/2}_X,\, F)$, where $X$ is a compact connected Riemann surface of genus $g$, with $g\, \geq\, 2$, $K^{1/2}_X$ is a theta characteristic on $X$, and $F$ is a…

A torsion free sheaf on a hyperk\"ahler variety $X$ is modular if the discriminant satisfies a certain condition, for example if it is a multiple of $c_2(X)$ the sheaf is modular. The definition is taylor made for torsion-free sheaves on a…