Related papers: Stable maps and Hurwitz schemes in mixed character…

In this paper we study planar hybrid systems composed by two stable linear systems, defined by Hurwitz matrices, in addition with a jump that can be a piecewise linear, a polynomial or an analytic function. We provide an explicit analytic…

In 1984, Charney and Lee defined a category of stable curves and exhibited a rational homology equivalence from its geometric realisation to (the analytification of) the moduli stack of stable curves, also known as the…

The study of the moduli of covers of the projective line leads to the theory of Hurwitz varieties covering configuration varieties. Certain one-dimensional slices of these coverings are particularly interesting Belyi maps. We present…

We provide a geometric construction of a sequence of modular blowups of the Artin stack parameterizing pre-stable pairs consisting of a genus-two nodal curve and a smooth divisor. The resulting stack locally diagonalizes the tautological…

Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the…

We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…

We introduce new logarithmic Hurwitz spaces $\mathcal{LH}^{\mathbb{Z}_{(p)}}_A$ and $\mathcal{LH}^{\mathbb{F}_{p}}_{A,\Xi}$ over $\mathbb{Z}_{(p)}$ and $\mathbb{F}_p$ respectively that in the mixed characteristic case can be considered as a…

This article is an extended version of preprint math.AG/9902104. We find an explicit formula for the number of topologically different ramified coverings of a sphere by a genus g surface with only one complicated branching point in terms of…

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 study moduli spaces of stable maps from pointed curves, where the points are allowed to coincide, with target a tame Deligne-Mumford stack. This generalizes the Abramovich-Vistoli theory of twisted stable maps as well as work of Hassett,…

We prove that the moduli space of stable maps of degree 2 to the moduli space of rank 2 stable bundles of fixed determinant O(-x) over a smooth projective curve of genus g>2 has two irre- ducible components which intersect transversely. One…

This note is but a research announcement, summarizing and explaining results proven and detailed in forthcoming papers. When one studies families of objects over curves, and the objects are parametrized by a Deligne-Mumford stack M, then…

In this paper we give a construction of algebraic (Artin) stacks endowed with a modular map onto the moduli stack of n-pointed stable curves of genus g, for g greater than 2. These stacks are smooth, irreducible and have dimension 4g-3+n,…

We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon observed for double…

For a given bundle $\xi \colon E \to M$ over a manifold, configuration-section spaces on $\xi$ parametrise finite subsets $z \subseteq M$ equipped with a section of $\xi$ defined on $M \smallsetminus z$, with prescribed "charge" in a…

We review the notion of stable supermap from SUSY curves to a fixed target superscheme, and prove that when the target is (super)projective, stable supermaps are parameterized by a Deligne-Mumford superstack with superschematic and…

Let $R$ be a complete discrete valuation ring of equal characteristic $p>0$. Given a $\mathbb{Z}/p$-Galois cover of a formal disc over $R$, one can derive from it a semi-stable model for which the specializations of branch points are…

For $2 \leq d \leq 5$, we show that the class of the Hurwitz space of smooth degree $d$, genus $g$ covers of $\mathbb P^1$ stabilizes in the Grothendieck ring of stacks as $g \to \infty$, and we give a formula for the limit. We also verify…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…

We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed…