The generic special scroll of genus g in Pn. Special scrolls in P3
We study the generic linearly normal special scroll of genus g in P^N. Moreover, we give a complete classification of the linearly normal scrolls in P^3 of genus 2 and 3.
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arXiv subjects
Manuel Pedreira Perez
Publications and source records attributed to Manuel Pedreira Perez.
Canonical Geometrically Ruled Surfaces
We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Teorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in P3. Canonical scrolls correspond to the projective model of canonical geometrically ruled surfaces over a smooth curve. We also prove that the generic canonical scroll is projectively normal except in the hyperelliptic case and for very particular cases in the nonhyperelliptic situation.
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Involutions of a canonical curve
We give a geometrical characterization of the ideal of quadrics containing a canonical curve with an involution. This implies to study involutions of rational normal scrolls and Veronese surfaces.
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Projective normality of special scrolls II
We study the projective normality of a linearly normal special scroll R of degree d and speciality i over a smooth curve X of genus g. We relate it with the Clifford index of the base curve X. If d>=4g-2i-Cliff(X)+1, i>=3 and R is smooth, we prove that the projective normality of the scroll is equivalent to the projective normality of its directrix curve of minimum degree.
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The Projective Theory of Ruled Surfaces
The aim of this paper is to get some results about ruled surfaces which configure a projective theory of scrolls and ruled surfaces. Our ideas follow the viewpoint of Corrado Segre, but we employ the contemporaneous language of locally free sheaves. The results complete the exposition given by R. Hartshorne and they have not appeared before in the contemporaneous literature.
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Dimension of the Moduli Space of curves with an involution
Given a smooth curve X of genus g we compute de dimension of the family of curves C which have an involution over X. Moreover we distinguish when the curve C is hyperelliptic.
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Projective normality of special scrolls
We study the projective normality of a linearly normal special scroll R of degree d and speciality i over a smooth curve of genus g. If d>=4g-2i+1, we prove that the projective normality of the scroll is equivalent to the projective normality of its directrix curve of minimum degree.
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