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Existence of good divisors on Mukai manifolds

Massimiliano Mella
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Abstract

A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, -K_X, is an ample Cartier divisor, the index of a Fano variety is the number i(X):=sup{t: -K_X= tH, for some ample Cartier divisor H}. Mukai announced, the classification of smooth Fano manifolds X of index i(X)=n-2, under the assumption that the linear system |H| contains a smooth divisor. In this paper we prove that this assumption is always satisfied. Therefore the result of Mukai provide a complete classification of smooth Fano n-folds of index $i(X)=n-2$, Mukai manifolds.

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Massimiliano Mella. 1996-11-20. Existence of good divisors on Mukai manifolds. https://arxiv.org/abs/alg-geom/9611024

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