On semistable Mori contractions

We study Mori fiber spaces over a two-dimensional base which satisfy the semistability assumption. As an application of our technique we give a new proof of the existence of semistable 3-fold flips.Comment: 14 pages, LaTeX2

Q-Fano threefolds of large Fano index, I

We study Q-Fano threefolds of large Fano index. In particular, we prove that the maximum of Fano index is attained for the weighted projective space P(3,4,5,7).Comment: 29 pages, latex, a few typos correcte

On Fano-Enriques threefolds

Let $U\subset \mathbb P^N$ be a projective variety which is not a cone and whose hyperplane sections are smooth Enriques surfaces. We prove that the degree of a $U$ is at most 32 and the bound is sharp.Comment: 18 pages, LaTe