Enumerative geometry of conics and double covers on projective complete intersections

Abstract

We compare genus zero degree two Gromov--Witten invariants with the number of embedded conics on general projective complete intersections whose conic space has expected dimension zero. Their difference comes from double covers of lines. We compute this contribution as an integral of Chern classes over the Fano scheme of lines, using an explicit obstruction bundle on the compactified space of double covers.