An inequality between multipoint Seshadri constants

TL;DR

This paper establishes a new inequality relating multipoint Seshadri constants on projective varieties, providing insights into their behavior with respect to multiple points and dimensions.

Contribution

It proves a novel inequality connecting Seshadri constants at multiple points, extending understanding of their properties on projective varieties.

Findings

Proves that e_d(rs;X,L) >= e_d(r;X,L) * e_d(s;P^n,O_{P^n}(1))

Provides a new inequality linking Seshadri constants at different scales

Enhances understanding of the behavior of Seshadri constants in algebraic geometry

Abstract

Let X be a projective variety of dimension n and L be a nef divisor on X. Denote by e_d(r;X,L) the d-dimensional Seshadri constant of r very general points in X. We prove that e_d(rs;X,L) >= e_d(r;X,L)e_d(s;P^n,O_{P^n}(1)).