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

Mikhail Grinenko
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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.

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Mikhail Grinenko. 2003-04-22. Non-rationality of a three-dimensional Fano variety of index 2 and degree 1. https://arxiv.org/abs/math/0304321

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