On the critical set for photogrammetric reconstruction using line tokens in P3(C)

Abstract

We prove that in general the critical set for photogrammetric reconstruction using lines in P 3 (C) is a line congruence Γ of order 3 and class 6; Γ has 10 singular points and no singular planes. The general hyperplane sections of Γ (ruled surfaces formed by intersecting Γ with linear line complexes) have genus 5. Γ can be found in Fano's classification of congruences of order 3, and further properties of Γ can be found in the literature.