# An invariant for embedded Fano manifolds covered by linear spaces

## TL;DR

This paper introduces a new invariant for embedded Fano manifolds related to linear spaces and aims to classify those with large invariant values.

## Contribution

It proposes a novel invariant $S_X$ for embedded Fano manifolds and provides a classification for manifolds with large $S_X$ values.

## Key findings

- Defined the invariant $S_X$ for embedded Fano manifolds.
- Classified Fano manifolds with large $S_X$ values.
- Connected the invariant to the geometry of covering linear spaces.

## Abstract

For an embedded Fano manifold $X$, we introduce a new invariant $S_X$ related to the dimension of covering linear spaces. The aim of this paper is to classify Fano manifolds $X$ which have large $S_X$.