Characterization of projective spaces by Seshadri constants

TL;DR

This paper characterizes complex projective spaces using Seshadri constants, proving that a variety is isomorphic to projective space if its anti-canonical divisor's Seshadri constant exceeds a certain threshold, and classifies varieties with equal constants.

Contribution

It establishes a new criterion for identifying projective spaces based on Seshadri constants and classifies varieties with specific constant values.

Findings

Varieties with Seshadri constant > n are isomorphic to projective space.

Classified varieties with Seshadri constant exactly equal to n.

Provided a characterization criterion for projective spaces.

Abstract

We prove that an $n$-dimensional complex projective variety is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than $n$. We also classify complex projective varieties with Seshadri constants equal to $n$.