We investigate a class of odd (ramification) coverings C → ℙ1 where is hyperelliptic, its Weierstrass points map to one fixed point and the covering makes hyperelliptic involution commute with an ℙ1. show that total number minimal degree 4g \(\left({\matrix{{3g} \cr {g - 1} \cr}} \right){2^{2g}}\) when general. Our study approached from three main perspectives: if effective theta characteristic...

In this work,we explore the theme of $$L^p$$ -boundedness Bergman projections domains that can be covered, in sense ramified coverings, by “nice” (e.g., strictly pseudoconvex with real analytic boundary). particular, we focus on two-dimensional normal coverings whose covering group is a finite unitary reflection group. an infinite family examples, are able to prove projection for every $$p\in (...

I give a survey about a program which intends to find topological characterizations of a rational map and then use them to study the rigidity problem for rational maps. Thurston started this program by considering critically finite branched coverings and gave a necessary and sufficient combinatorial condition for a critically finite rational maps among all critically finite branched coverings. ...

In this paper we introduce the notion of an extensive 2-category, to be thought of as a “2-category of generalized spaces”. We consider an extensive 2-category K equipped with a binary-product-preserving pseudofunctor C : K op → CAT, which we think of as specifying the “coverings” of our generalized spaces. We prove, in this context, a van Kampen theorem which generalizes and refines one of Bro...

We consider the action of mapping class groups, by preand postcomposition, on branched coverings, and encode them algebraically as mapping class bisets. We show how the mapping class biset of maps preserving a multicurve decomposes into mapping class bisets of smaller complexity, called small mapping class bisets. We phrase the decision problem of Thurston equivalence between branched self-cove...

Enumerating ramified coverings of the sphere with fixed ramification types is a well-known problem first considered by A. Hurwitz [5]. Up to now, explicit solutions have been obtained only for some families of ramified coverings, for instant, those realized by polynomials in one complex variable. In this paper we obtain an explicit answer for a large new family of coverings, namely, the coverin...

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algor...