Infinitesimal deformations of double covers of smooth algebraic varieties (original) (raw)

This research presents a method for computing the space of infinitesimal deformations of double covers of smooth algebraic varieties. The focus lies on the relationship between such deformations and the geometry of the underlying varieties, particularly in the context of Calabi-Yau manifolds derived from double covers of P3 branched along singular octic surfaces. Key results include a distinction between various subspaces of infinitesimal deformations and the identification of transverse deformations that influence the branching locus.