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On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces

Nariya Kawazumi (1993)

Annales de l'institut Fourier

The continuous cohomology theory of the Lie algebra L ( M ) of complex analytic vector fields on an open Riemann surface M is studied. We show that the cohomology group with coefficients in the L ( M ) -module of germs of complex analytic tensor fields on the product space M n decomposes into the global part derived from the homology of M and the local part coming from the coefficients.

On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.

Antonio F. Costa, Milagros Izquierdo, Daniel Ying (2007)

RACSAM

A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs...

On the topological triviality along moduli of deformations of J k , 0 singularities

Piotr Jaworski (2000)

Annales Polonici Mathematici

It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results of J....

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