514 research outputs found
Classification of Incidence Scrolls (II)
The aim of this paper is to obtain a classification of the scrolls in Pn
which are defined by a one-dimensional family of lines meeting a certain set of
linear spaces in Pn, a first classification for genus 0 and 1 is given in paper
[1]. These ruled surfaces are called incidence scrolls, and such an indicated
set is a base of the incidence scroll. In particular, we compute its degree and
genus. For this, we define the fundamental incidence scroll to be the scroll in
Pn formed by the lines which meet (2n-3) P{n-2}'s in general position. Then all
the others incidence scrolls will be portions of degenerate forms of this. In
this way, we can obtain all the incidence scrolls in Pn, n>2, with base in
general position.Comment: 22 page
Classification of Incidence Scrolls(I)
The aim of this paper is to obtain a classification of scrolls of genus 0 and
1, which are defined by a one-dimensional family of lines meeting a certain set
of linear spaces in . These ruled surfaces will be called incidence
scrolls and such a set will be the base of the incidence scroll. Unless
otherwise stated, we assume that the base spaces are in general position.Comment: Latex209, 19 pages, revised and corrected version. To appear in
Manuscripta Mathematic
Another classification of Incidence Scrolls
The aim of this paper is the computation of the degree and genus of all
incidence scrolls in Pn. For this, we fix the dimension of a linear space which
have a base space of this fixed dimension. In this way, we can obtain all the
incidence scrolls with a line as directrix curve, those whose base contains a
plane, and so on.Comment: Latex, 10 pages. It contains three tables. Accepted for publication
in Archiv der Mathemati
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.Comment: 40 page
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.Comment: Submitted for publicatio
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.Comment: 7 page
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.Comment: 7 page
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.Comment: 20 page
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.Comment: Latex2.09; 32 page
Projective generation and smoothness of congruences of order 1
In this paper we give the projective generation of congruences of order 1 of
r-dimensional projective spaces in P^N from their focal loci. In a natural way,
this construction shows that the corresponding surfaces in the grassmannian are
the Veronese surface, and rational ruled surfaces eventually with
singularities. We characterize when these surfaces are smooth, recovering and
generalizing a Ziv Ran's result.Comment: Latex2e, 18 page
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