On a Grauert-Riemenschneider vanishing theorem for Frobenius split varieties in characteristic p.
On abelian subvarieties generated by symmetric correspondences.
On connected divisors.
On the Castelnuovo-Mumford regularity of products of ideal sheaves.
On the k-regularity of some proyective manifolds.
The conjecture on the (degree-codimension + 1) - regularity of projective varieties is proved for smooth linearly normal polarized varieties (X,L) with L very ample, for low values of Delta(X,L) = degree-codimension-1. Results concerning the projective normality of some classes of special varieties including scrolls over curves of genus 2 and quadric fibrations over elliptic curves, are proved.