Singularities of Generic Line Congruences

2021/08/14 by Marcos Craizer, Craizer, Marcos, Ronaldo Garcia +1 · 1 citation
Mathematics · #53A20 #53A55 #57R45 #Commutative Algebra and Its Applications #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2108.06525

openalex publication_date 2021/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Line congruences are 2-dimensional families of lines in 3-space. The singularities that appear in generic line congruences are folds, cusps and swallowtails. In this paper we give a geometric description of these singularities. The main tool used is the existence of an equiaffine pair defining a generic line congruence.

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