Smooth $l$-Fano weighted complete intersections

Abstract

In this paper we prove that for $n$-dimensional smooth $l$-Fano well-formed weighted complete intersections that are 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 variety of dimension $n$ among such manifolds, where $\lceil {\log }_3(n+2)\rceil ⩽l⩽\lceil {\log }_2(n+2)\rceil -1$, is a complete intersection of quadrics in a usual projective space.