$D_5$ elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory

Abstract

elliptic fibration is a fibration whose generic fiber is modeled by the complete intersection of two quadric surfaces in P 3 . They provide simple examples of elliptic fibrations admitting a rich spectrum of singular fibers (not all on the list of Kodaira) without introducing singularities in the total space of the fibration, thus avoiding a discussion of their resolutions. We study systematically the fiber geometry of such fibrations using Segre symbols and compute several topological invariants.