Vanishing theorems and degeneracy loci in small corang. (Théoremès d'annulation et lieux de degenerescence en petit corang.)
Varieities with low dimensional dual variety.
Varieties of minimal rational tangents of codimension 1
Let be a uniruled projective manifold and let be a general point. The main result of [2] says that if the -degrees (i.e., the degrees with respect to the anti-canonical bundle of ) of all rational curves through are at least , then is a projective space. In this paper, we study the structure of when the -degrees of all rational curves through are at least . Our study uses the projective variety , called the VMRT at , defined as the union of tangent directions to the rational curves...
Varieties with an extremal number of degenerate higher secant varieties.
Varieties with many lines.
Varieties with small dual varieties, I.
Vector spaces of matrices of low rank and vector bundles on projective spaces: An addendum to a paper by Eisenbud and Harris.
Very ample line bundles on blown-up projective varieties.