Related papers: Boundary behaviour of Hurwitz schemes

Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…

Topological phenomena are commonly studied in phases of matter which are separated from a trivial phase by an unavoidable quantum phase transition. This can be overly restrictive, leaving out scenarios of practical relevance -- similar to…

We use the equivariant Yang-Mills moduli space to investigate the relation between the singular set, isotropy representations at fixed points, and permutation modules realized by the induced action on homology for smooth group actions on…

We survey some results concerning finite group actions on products of spheres.

Given an automorphism of a smooth complex algebraic curve, there is an induced action on the moduli space of semi-stable rank 2 holomorphic bundles with fixed determinant. We give a complete description of the fixed variety in terms of…

We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…

We study flips of moduli schemes of stable torsion free sheaves as wall-crossing phenomena of moduli schemes of stable modules over certain finite dimensional algebra. They are described as stratified Grassmann bundles.

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general…

In the present paper, we study a new kind of anabelian phenomenon concerning the smooth pointed stable curves in positive characteristic. It shows that the topological structures of moduli spaces of curves can be understood from the…

In anabelian geometry, we consider to what extent the \'{e}tale or tame fundamental groups of schemes reflect geometric properties of the schemes. Although there are many known results (mainly for smooth curves) in this area, general…

A unified treatment is given of some results of H. Donnelly-P. Li and L. Schwartz concerning the behaviour of heat semigroups on open manifolds with given compactifications, on one hand, and the relationship with the behaviour at infinity…

We show that if a hyperbolic group acts geometrically on a CAT(0) cube complex, then the induced boundary action is hyperfinite. This means that for a cubulated hyperbolic group the natural action on its Gromov boundary is hyperfinite,…

G\"ottsche gave a formula for the dimension of the cohomology of Hilbert schemes of points on a smooth projective surface $S$. When $S$ admits an action by a finite group $G$, we describe the action of $G$ on the Hodge structure. In the…

For some class of mappings satisfying upper modular estimates with respect to families of curves, a behavior of the corresponding inverse mappings is investigated. In the terms of prime ends, it is proved that, families of such…

Abramovich, Corti and Vistoli have studied modular compactifications of stacks of curves equipped with abelian level structures arising as substacks of the stack of twisted stable maps into the classifying stack of a finite group, provided…

It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence…

For every Cuntz--Krieger groupoid, we show that there is a topologically free boundary action of the outer automorphism group of its topological full group on the Hilbert cube. In particular, these outer automorphism groups, including the…

In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…

This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles…

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…