Related papers: Open problems (for AGNES)

This is a slightly revised version of the author's 2010 diploma thesis. It is concerned with the interplay between real multiplication on Jacobian varieties, as the title suggests, and complex geodesics in the moduli space of curves. Large…

We consider modular properties of nodal curves on general $K3$ surfaces. Let $\mathcal{K}_p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\geqslant 3$ and $\mathcal{V}_{p,m,\delta}\to \mathcal{K}_p$ be the…

We study relationships between the Nisnevich topology on smooth schemes and certain Grothendieck topologies on proper and not necessarily proper modulus pairs which were introduced respectively in [9] and [3]. Our results play an important…

We construct a moduli space of adequately marked Enriques surfaces that have a supersingular K3 cover over fields of characteristic $p \geq 3$. We show that this moduli space exists as a scheme locally of finite type over $\mathbb{F}_p$.…

We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a weak analog of the Keel-Mori theorem, which guarantees the existence of a coarse moduli space for a separated…

We provide new examples of anti-symplectic involutions on moduli spaces of stable sheaves on K3 surfaces. These involutions are constructed through (anti) autoequivalences of the bounded derived category of coherent sheaves on K3 surfaces…

In this paper, we consider moduli spaces of stable sheaves on abelian surfaces. Our main assumption is the primitivity of the associated Mukai vector. We construct many isomorphisms of muduli spaces induced by Fourier-Mukai functor. As an…

The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and…

We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropical curves, and establish some of its basic topological properties. We compare it to…

We study the moduli space of genus 3 hyperelliptic curves via the weighted projective space of binary octavics. This enables us to create a database of all genus 3 hyperelliptic curves defined over $\mathbb Q$, of weighted moduli height…

We shall study the existence condition of slope stable sheaves on Enriques surfaces. We also gives a different proof of the irreducibility of the moduli spaces of rank 2 stable sheaves.

To every oriented tree, we associate a moduli problem for sheaves over a projective manifold $X$. We define the corresponding notion of semistability and establish the existence of moduli spaces. Applying the results to the tree *->*, we…

We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct…

Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.

In this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If $S$ is a K3, $v=2w$ is a Mukai vector on $S$, where $w$ is primitive and $w^{2}=2$, and $H$ is a $v-$generic polarization on $S$, then the moduli…

We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.

We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on…

We extend a previous result of Feyzbakhsh concerning the injectivity of a map of moduli spaces and we use this result to construct curves whose Brill-Noether loci have unexpected dimension.

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can…

It was suggested on several occasions by Deligne, Drinfeld and Kontsevich that all the moduli spaces arising in the classical problems of deformation theory should be extended to natural "derived" moduli spaces which are always smooth in an…