On the Picard Group of Low-codimension Subvarieties

Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group Z

We investigate a method proposed by E. Arrondo and J. Caravantes to study the Picard group of a smooth lowcodimension subvariety X in a variety Y when Y is homogeneous. We prove that this method is strongly related to the signature σY of the Poincaré pairing on the middle cohomology of Y . We give under some topological assumptions a bound on the rank of Picard group Pic(X) in terms of σY and r...

Lifting Problem in Codimension 2 and Initial Ideals

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.

Anomalous Subvarieties—Structure Theorems and Applications

When a fixed algebraic variety in a multiplicative group variety is intersected with the union of all algebraic subgroups of fixed dimension, a key role is played by what we call the anomalous subvarieties. These arise when the algebraic variety meets translates of subgroups in sets larger than expected. We prove a Structure Theorem for the anomalous subvarieties, and we give some applications,...

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.