On birational involutions of P3P^3

Let $X$ be a rationally connected three-dimensional algebraic variety and let $\tau$ be an element of order two in the group of its birational selfmaps. Suppose that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program we give a rough classification of such elements.Comment: 24 pages, late

Fano threefolds of large Fano index and large degree

We classify Q-Fano threefolds of Fano index > 2 and big degree.Comment: 38 page