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On curves with natural cohomology and their deficiency modules

Giorgio Bolondi, Jean-Claude Migliore (1993)

Annales de l'institut Fourier

The minimal free resolution of the Hartshorne-Rao module of a curve with natural cohomology is studied, and conditions are given on the degrees and the ranks of the terms of this resolution.

On ramified covers of the projective plane II: Generalizing Segre’s theory

Michael Friedman, Rebecca Lehman, Maxim Leyenson, Mina Teicher (2012)

Journal of the European Mathematical Society

The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in 3 . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, B and E , we give a necessary and sufficient condition for B to be the branch curve of a surface X in N and E to be the image of the double curve of a 3 -model of X . In the classical Segre theory, a plane curve...

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

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