Hilbert Schemes and Seshadri Constants

TL;DR

This paper introduces a novel approach to studying Seshadri constants using nested Hilbert schemes, leveraging their geometric properties and stability conditions to derive new bounds and insights.

Contribution

It proposes a new method connecting Seshadri constants with Hilbert schemes and their stability conditions, providing a fresh perspective and tools for their analysis.

Findings

Many known Seshadri constants appear in the wall and chamber decomposition of Hilbert schemes' movable cone.

The method enables computation of nef cones via Bridgeland stability conditions.

New bounds on Seshadri constants are obtained through geometric analysis of Hilbert schemes.

Abstract

In this paper we will propose a new method to investigate Seshadri constants, namely by means of (nested) Hilbert schemes. This will allow us to use the geometry of the latter spaces, for example the computations of the nef cone via Bridgeland stability conditions to gain new insights and bounds on Seshadri constants. Moreover, it turns out that many known Seshadri constants turn up in the wall and chamber decomposition of the movable cone of Hilbert schemes.