Projective generation and smoothness of congruences of order 1

Details Projective generation and smoothness of congruences of order 1 Projective generation and smoothness of congruences of order 1

2000-03-08

arxiv.org/abs/math/0003048v1

Mathematics

Algebraic Geometry

Latex2e, 18 pages

Scientific paper

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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