On the automorphism groups of algebraic bounded domains.
Let C be a smooth curve of genus g. For each positive integer r the birational r-gonality sr(C) of C is the minimal integer t such that there is L ∈ Pict(C) with h0(C,L) = r + 1. Fix an integer r ≥ 3. In this paper we prove the existence of an integer gr such that for every integer g ≥ gr there is a smooth curve C of genus g with sr+1(C)/(r + 1) > sr(C)/r, i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails
Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.
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.