Seshadri constants and related conjectures over characteristic zero fields

Abstract

In this article, we study Seshadri constants over a base field k, which is of characteristic zero and not necessarily algebraically closed. We provide an upper bound for them and also discuss their behaviour under base change. Additionally, we examine Segre's Conjecture, Harbourne-Hirschowitz's Conjecture, and Nagata's Conjecture, discussing their interrelations in this setting.