Projective generation and smoothness of congruences of order 1
Manuel Pedreira-Perez, Luis-Eduardo Sola-Conde
Abstract
In this paper we give the projective generation of congruences of order 1 of r-dimensional projective spaces in PN 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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