BOUNDEDNESS FOR CODIMENSION TWO SUBVARIETIES

Abstract

We prove that for certain projective varieties V ⊂ Pr (e.g. smooth complete intersections with dim (V) ≥ 4, or complete intersections with dim (V) ≥ 7 and codim V ( Sing (V)) ≥ 6), there are only finitely many components of the Hilbert scheme parametrizing irreducible, smooth, projective, codimension two subvarieties of V not of general type.