Rationality of an Enriques-Fano threefold of genus five

摘要

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 Z. This threefold can be described as the quotient of a double covering of P-3 ramified in a smooth quartic surface by an involution fixing eight different points.