Non-rationality of a three-dimensional Fano variety of index 2 and degree 1

Details Non-rationality of a three-dimensional Fano variety of index 2 and degree 1 Non-rationality of a three-dimensional Fano variety of index 2 and degree 1

2003-04-22

arxiv.org/abs/math/0304321v1

Mathematics

Algebraic Geometry

24 pages, 3 figures

Scientific paper

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.

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