Non-rationality of a three-dimensional Fano variety of index 2 and degree 1
arXiv:math/0304321
Abstract
We describe the set of Mori structures for a Fano 3-fold of index 2 and degree 1 (the double cone over the Veronese surface). In partiular, it is proved that such a Fano variety is not rational, the group of birational automorphisms coincides with the group of biregular automorphisms, and there are no structures of conic bundle.
24 pages, 3 figures