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On the birational gonalities of smooth curves

E. Ballico (2014)

Annales UMCS, Mathematica

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

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.

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