An inequality between multipoint Seshadri constants

Abstract

Let X be a projective variety of dimension n and L be a nef divisor on X. Denote by \({\epsilon_d(r; X, L)}\) the d-dimensional Seshadri constant of r very general points in X. We prove that $$\epsilon_d(rs;X,L)\geq \epsilon_d(r;X,L)\cdot \epsilon_d(s;\mathbb {P}^n,\mathcal {O}_{\mathbb {P}^n}(1)) \quad \text{for}\,r, s\geq 1.$$