Projective generation and smoothness of congruences of order 1

2000/03/08 by Manuel Pedreira-Perez, Pedreira-Perez, Manuel, Luis-Eduardo Sola-Conde +1
Mathematics · #14J #14M15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J #msc:14M15

paper · pdf · doi:10.48550/arxiv.math/0003048

Latex2e, 18 pages

arxiv created 2000/03/08 · arxiv updated 2009/11/30

Abstract

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.

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