Normalization of congruence of bitangents to a hypersurface in ${\mathbb{P}}^3$

Abstract

A congruence is a surface in the Grassmannian $\mathrm{Gr}(2,4)$. In this paper, we consider the normalization of congruence of bitangents to a hypersurface in ${\mathbb{P}}^3$. We call it the Fano congruence of bitangents. We give a criterion for smoothness of the Fano congruence of bitangents and describe explicitly their degenerations in a general Lefschetz pencil in the space of hypersurfaces in ${\mathbb{P}}^3$.

16 pages