Existence of good divisors on Mukai manifolds
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)=n2, 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 nfolds of index $i(X)=n2$, Mukai manifolds.
 Publication:

arXiv eprints
 Pub Date:
 November 1996
 arXiv:
 arXiv:alggeom/9611024
 Bibcode:
 1996alg.geom.11024M
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 LaTex, 12 pages, nofig