Smooth $l$-Fano weighted complete intersections

In this paper we prove that for $n$-dimensional smooth $l$-Fano well-formed weighted complete intersections that are not isomorphic to an 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 $\lceil \log_3(n+2) \rceil\leqslant l \leqslant \lceil \log_2(n+2) \rceil -1$, is a complete intersection of quadrics in an usual projective space. Bibliography: 17 titles.