K\"ahler packings and Seshadri constants on projective complex surfaces

TL;DR

This paper establishes a connection between multiple point Seshadri constants on projective complex surfaces and the supremum of radii of multiple K"ahler ball embeddings, drawing an analogy with symplectic packings and blow ups.

Contribution

It introduces a novel method to compute Seshadri constants via K"ahler packings, extending the analogy with symplectic geometry to algebraic geometry.

Findings

Seshadri constants can be expressed as supremums of K"ahler ball embedding radii.

Provides a new geometric interpretation of Seshadri constants on complex surfaces.

Establishes an analogy between symplectic and algebraic geometric concepts.

Abstract

In analogy to the relation between symplectic packings and symplectic blow ups we show that multiple point Seshadri constants on projective complex surfaces can be calculated as the supremum of radii of multiple K\"ahler ball embeddings.