Related papers: Geometry of some moduli of bundles over a very gen…

Let M(v) be the moduli of stable sheaves on K3 surfaces X of Mukai vector v. If v is primitive, than it is expected that M(v) is deformation equivalent to some Hilbert scheme and weight two hogde structure can be described by H^*(X,Z).…

We propose a three-step program for the classification of stable rank 2 bundles on the projective space $\mathbb{P}^3$ inspired by an article by Hartshorne and Rao. While this classification program has been successfully completed for…

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli…

We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…

We consider smooth moduli spaces of semistable vector bundles of fixed rank and determinant on a compact Riemann surface $X$ of genus at least $3$. The choice of a Poincar\'e bundle for such a moduli space $M$ induces an isomorphism between…

A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2; \mathbb{C})$, a resolution $Y$ of $\mathbb{C}^2/G$ is isomorphic to a moduli space $\mathcal{M}_{\theta}$ of $G$-constellations for some generic stability parameter…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…

In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis…

Newstead and Ramanan conjectured the vanishing of the top (2g-1) Chern classes of the moduli space of stable, odd degree vector bundles of rank 2 on a Riemann surface of genus g. This was proved by Gieseker [G], while an analogue in rank 3…

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 prove that the modular component $\mathcal M(r)$, constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank $r$ and given Chern classes,…

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

We give a complete description of the two-dimensional moduli spaces of stable Higgs bundles of rank 2 over complex projective line with one irregular singular point, having a regular leading-order term, and endowed with a generic compatible…

We prove that any class $VII$ surface with $b_2=1$ has curves. This implies the "Global Spherical Shell conjecture" in the case $b_2=1$: Any minimal class $VII$ surface with $b_2=1$ admits a global spherical shell, hence it is isomorphic to…

Let $C$ be a curve with two smooth components and a single node. Let $\mathcal{U}_C(r,w,\chi)$ be the moduli space of $w$-semistable classes of depth one sheaves on $C$ having rank $r$ on both components and Euler characteristic $\chi$. In…

We study the moduli space of minimal surfaces of general type with $K_S^2 = 1$ and $p_g = 2$ and show that it is irreducible, has dimension $28$ and admits a compactification which is unirational.

We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider a natural involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C} \mathbb{P}^1$ and…