Ordinary Subvarieties of Codimension One

Points in Generic Position and Conductor of Varieties with Ordinary Multiple Subvarieties of Codimension One

We extend results of our previous papers, on ordinary multiple points of curves [9], and on the computation of their conductor [8], to ordinary multiple subvarieties of codimension one.

Lifting Problem in Codimension 2 and Initial Ideals

Adjoint Ideals along Closed Subvarieties of Higher Codimension

In this paper, we introduce a notion of adjoint ideal sheaves along closed subvarieties of higher codimension and prove a restriction property of our adjoint ideal sheaves using characteristic p methods.

Subcanonicity of Codimension Two Subvarieties

We prove that smooth subvarieties of codimension two in Grassmannians of lines of dimension at least six are rationally numerically subcanonical. We prove the same result for smooth quadrics of dimension at least six under some extra condition. The method is quite easy, and only uses Serre’s construction, Porteous formula and Hodge index theorem.

Degrees of High-dimensional Subvarieties of Determinantal Varieties

Let n = pab, where p is a prime, and g.c.d.(p, b) = 1. In Pn −1, let Xr be the variety defined by rank((xi,j)) ≤ n − r. We show that any subvariety of Xr of codimension less than par must have degree a multiple of p. We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are