Non-reduced components of the Noether-Lefschetz locus

Original · EN

For a fixed integer d ≥ 5, the Noether-Lefschetz locus parametrizes smooth degree d complex hypersurfaces in P³ with Picard number greater than 1. There are infinitely many irreducible components of this locus. The aim of this article is to understand the scheme structure of these components. In particular, we study when is such a component non-reduced. We give a criterion for such a component to be non-reduced. Finally, we give examples of such components.