arXiv subjects

Manuel Pedreira-Perez

Publications and source records attributed to Manuel Pedreira-Perez.

3 recordsLinked to original sources

arXiv2000

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.

math.AG↗

arXiv1999

Classification of Plane Congruences in P4(C) (I)

Nondegenerate plane congruences in the four-dimensional complex projective space with degenerate general focal conic are classified by using the focal method due to Corrado Segre.

math.AG↗

arXiv1999

Classification of Plane Congruences in P4(C) (II)

We study second order focal loci of nondegenerate plane congruences in P4(C) with degenerate focal conic. We show the projective generation of such congruences when the second order focal locus fills a component of the focal conic, improving a result of Corrado Segre

math.AG↗