Subcanonicity of Codimension Two Subvarieties

Lifting Problem in Codimension 2 and Initial Ideals

On Codimension Two Subvarieties in Hypersurfaces

We show that for a smooth hypersurface X ⊂ P of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties Y ⊂ X which are not an intersection X ∩ S for a codimension two subvariety S ⊂ P. We also show there exist Y ⊂ X as above for which the normal bundle sequence for the inclusion Y ⊂ X ⊂ P does not split. Dedicated to Spencer Bloch

On a Special Class of Smooth Codimension Two Subvarieties

We work on an algebraically closed field of characteristic zero. By Lefschetz’s theorem, a smooth codimension two subvariety X ⊂ P, n ≥ 4, which is not a complete intersection, lying on a hypersurface Σ, verifies dim(X ∩ Sing(Σ)) ≥ n− 4. In this paper we deal with a situation in which the singular locus of Σ is as large as can be, but, at the same time, the simplest possible: we assume Σ is an ...

Ordinary Subvarieties of Codimension One

In this paper we extend the properties of ordinary points of curves [10] to ordinary closed points of one-dimensional affine reduced schemes and then to ordinary subvarieties of codimension one.

Boundedness for Codimension Two Submanifolds of Quadrics

It is proved that there are only finitely many families of codimension two subvarieties not of general type in Q6.