Normalization of the congruence of bitangents to a hypersurface in P3

Abstract

© 2022 Elsevier B.V.A surface in the Grassmannian Gr(2,4) is called a congruence. In this paper, we consider the normalization of the congruence of bitangents to a hypersurface in P3. 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 P3.