Related papers: Hurwitz-Ran spaces
We prove that any connected component of the space of m-spin structures on compact Riemann surfaces with finite number of punctures and holes is homeomorphic to a quotient of the vector space R^d by a discrete group action. Our proof is…
We study double Hurwitz numbers in genus zero counting the number of covers $\CP^1\to\CP^1$ with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise…
In this series of papers, we investigate a new anabelian phenomenon of curves over algebraically closed fields of positive characteristic. Let $\overline M_{g, n}$ be the moduli space of curves of type $(g, n)$ over $\overline…
In this paper, we construct a function which confirms the proper inclusion property of Morrey spaces, by using a relation between a class of functions in Morrey spaces and discrete Morrey spaces. Our particular function is simpler than…
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology…
We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…
We give a metric characterisation of when the Lipschitz-free space over a separable ultrametric space is a dual Banach space. In the case where the Lipschitz-free space has a predual, we show that this predual is M-embedded if and only if…
We consider the Hurwitz spaces of ramified coverings of $\mathbb{P}^1$ with prescribed ramification profile over the point at infinity. By means of a particular symmetric bidifferential on a compact Riemann surface, we introduce…
We study the compactly supported rational cohomology of configuration spaces of points on wedges of spheres, equipped with natural actions of the symmetric group and the group $Out(F_g)$ of outer automorphisms of the free group. These…
The aim of this article is to characterize pairs of curves within multiplicative (non-Newtonian) spaces. Specifically, we investigate how famous curve pairs such as Bertrand partner curves, Mannheim partner curves, which are prominent in…
In this paper we study the cohomology of PEL-type Rapoport-Zink spaces associated to unramified unitary similitude groups over $\Q_p$ in an odd number of variables. We extend the results of Kaletha-Minguez-Shin-White to construct a local…
We give a necessary condition for inclusion relations between discrete Morrey spaces which can be seen as a complement of the results in \cite{GKS,HS2}. We also prove another inclusion property of discrete Morrey spaces which can be viewed…
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric…
The Hurwitz space $\overline{\mathscr{H}}_{k,g}$ is a compactification of the space of smooth genus-$g$ curves with a simply-branched degree-$k$ map to $\mathbb{P}^1$. In this paper, we initiate a study of the Chow rings of these spaces,…
In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with $0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals…
Motivated by recent work on the use of topological methods to study collections of rings between an integral domain and its quotient field, we examine spaces of subrings of a commutative ring, where these spaces are endowed with the Zariski…
The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…
The family of quads of interrelated functions holomorphic on the universal cover of the complex plane without zero (for brevity, pqrs-functions), revealing a number of remarkable properties, is introduced. In particular, under certain…
Given an algebraic variety X defined over an algebraically closed field, we study the space RZ(X,x) consisting of all the valuations of the function field of X which are centered in a closed point x of X. We concentrate on its homeomorphism…
We study the Golomb spaces of Dedekind domains with torsion class group. In particular, we show that a homeomorphism between two such spaces sends prime ideals into prime ideals and preserves the $P$-adic topology on $R\setminus P$. Under…