On a conjecture of Mukai.
On a spanned tautological bundle.
On Bănică sheaves and Fano manifolds
On contractions of extremal rays of Fano manifolds.
On del Pezzo fibrations
On Fano 3-Folds.
On Fano 4-folds of index 1 and homogeneous vector bundles over Grassmannians.
On Fano Manifolds of large index.
On geometry of binary symmetric models of phylogenetic trees
We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for...
On some numerical properties of Fano varieties
This is the text of a talk given at the XVII Convegno dellUnione Matematica Italiana held at Milano, September 8-13, 2003. I would like to thank Angelo Lopez and Ciro Ciliberto for the kind invitation to the conference. I survey some numerical conjectures and theorems concerning relations between the index, the pseudo-index and the Picard number of a Fano variety. The results I refer to are contained in the paper [3], wrote in collaboration with Bonavero, Debarre and Druel.
On some special Fano manifolds.
On the discriminant locus of an ample and spanned line bundle.
On the Picard number of divisors in Fano manifolds
Let be a complex Fano manifold of arbitrary dimension, and a prime divisor in . We consider the image of in under the natural push-forward of -cycles. We show that . Moreover if , then either where is a Del Pezzo surface, or and has a fibration in Del Pezzo surfaces onto a Fano manifold such that .
On the second exterior power of tangent bundles of threefolds
On the stability of the tangent bundle of Fano manifolds.