Marco Andreatta

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex iX and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(iX−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex iX≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.

Special rays in the Mori cone of a projective variety

Let X be a smooth n -dimensional projective variety over an algebraically closed field k such that K X is not nef. We give a characterization of non nef extremal rays of X of maximal length (i.e of length n – 1); in the case of Char( k ) = 0 we also characterize non nef rays of length n – 2.

Contractions on a manifold polarized by an ample vector bundle

A complex manifold

Some remarks on the study of good contractions

X

Ample vector bundles with sections vanishing on special varieties

of dimension

4-dimensional symplectic contractions

n

MINIMAL MODEL PROGRAM WITH SCALING AND ADJUNCTION THEORY

together with an ample vector bundle

On the 2 very ampleness of the adjoint bundle

E

FANO-MORI CONTRACTIONS OF HIGH LENGTH ON PROJECTIVE VARIETIES WITH TERMINAL SINGULARITIES

on it will be called a {\sf generalized polarized variety}. The adjoint bundle of the pair

On the adjunction process over a surface in char.p

(X,E)