Smooth $l$-Fano weighted complete intersections

Abstract

In this paper we prove that for $n$-dimensional smooth $l$-Fano well formed weighted complete intersections, which is not isomorphic to a usual projective space, the upper bound for $l$ is equal to $\lceil {\log }_2(n+2)\rceil -1.$ We also prove that the only $l$-Fano of dimension $n$ among such manifolds with inequalities $\lceil {\log }_3(n+2)\rceil ⩽l⩽\lceil {\log }_2(n+2)\rceil -1$ is a complete intersection of quadrics in a usual projective space.