Rationality of an Enriques--Fano threefold of genus five

I. A. Cheltsov

Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 607-618.

Résumé

We prove the rationality of a non-Gorenstein Fano threefold of Fano index one and degree eight having terminal cyclic quotient singularities and Picard group $\mathbb Z$. This threefold can be described as the quotient of a double covering of $\mathbb P^3$ ramified in a smooth quartic surface by an involution fixing eight different points.

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