Smooth $l$-Fano weighted complete intersections

TL;DR

This paper establishes an upper bound on the parameter l for smooth l-Fano weighted complete intersections and characterizes those with specific l values as quadrics in projective space.

Contribution

It proves a new upper bound for l in smooth l-Fano weighted complete intersections and classifies certain cases as quadrics in projective space.

Findings

Upper bound for l is   \, ext{log}_2(n+2)  - 1.

Only quadrics in projective space occur for specific l ranges.

Classifies smooth l-Fano weighted complete intersections not isomorphic to projective space.

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 \leqslant l \leqslant \lceil \log_2(n+2) \rceil -1 $ is a complete intersection of quadrics in a usual projective space.