We study a class of new examples of congruences of lines of order one, i.e. the congruences associated to the completely exceptional Monge-Ampère equations. We prove that they are in general not linear, and that through a general point of the focal locus there passes a planar pencil of lines of the congruence. In particular, the completely exceptional Monge-Ampère equations are of Temple type.
"On a class of first order congruences of lines." Bull. Belg. Math. Soc. Simon Stevin 16 (5) 805 - 821, December 2009. https://doi.org/10.36045/bbms/1260369400