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The moduli spaceM g of compact Riemann surfaces of genus g has the structure of an orbifold and the set of singular points of such orbifold is thebranch locus B g. In this article we present some results related with the topology ofB g. We study the connectedness ofB g forg ≤ 8, the existence of isolated equisymmetric strata in the branch loci and finally we stablish the connectedness of the...
The moduli space $$ \mathcal{M}_g $$ of compact Riemann surfaces of genus g has the structure of an orbifold and the set of singular points of such orbifold is the branch locus $$ \mathcal{B}_g $$ . In this article we present some results related with the topology of $$ \mathcal{B}_g $$ . We study the connectedness of $$ \mathcal{B}_g $$ for g ≤ 8, the existence of isolated equisymmetric...
Let $${\phi }$$ be an automorphism of prime order of a group G. If its fixed-point set $${\rm C}{_{\rm G}(\phi)}$$ is finite, then frequently G is nilpotent-by-finite. If $${\rm C}{_{\rm G}(\phi )}$$ is periodic, then sometimes the commutator subgroup [G, $${\phi }$$ ] of $${\phi }$$ is periodic-by-nilpotent, indeed occasionally G itself is periodic-by-nilpotent. Here, if...
Since every Riemann surface admits a meromorphic function then Riemann surfaces (algebraic curves) can be viewed as branched coverings of the Riemann sphere $$\mathbb {\hat{C}}$$ C ^ . A morphism from a Riemann surface on $$\mathbb {\hat{C}}$$ C ^ of degree $$n$$ n is called an $$n$$ n -gonal morphism. If $$p$$ p is a prime and there is a $$p$$ ...
In the paper, the spectra of weighted composition operators on Hardy-type spaces of holomorphic functions on the unit disc of the complex plane are studied. The spectra of invertible operators induced by elliptic and parabolic automorphisms are described, for weighted composition operators acting on abstract Hardy spaces generated by Banach lattices. We also study spectra of weighted composition operators...
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