On deformations of monomial curves
On period relations for abelian integrals on algebraic curves
On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces
The continuous cohomology theory of the Lie algebra of complex analytic vector fields on an open Riemann surface is studied. We show that the cohomology group with coefficients in the -module of germs of complex analytic tensor fields on the product space decomposes into the global part derived from the homology of and the local part coming from the coefficients.
On the connectedness of the locus of real Riemann surfaces.
On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.
On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.
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 Kodaira Dimension of the Moduli Space of Curves.
On the topological triviality along moduli of deformations of singularities
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....