# Asymptotics of linear systems, with connections to line arrangements

## TL;DR

This paper explores the asymptotic behavior of linear systems influenced by line arrangements, addressing key problems like symbolic power containment and bounded negativity, and offering new insights into longstanding conjectures.

## Contribution

It introduces novel connections between line arrangements and asymptotic invariants, providing fresh perspectives on the SHGH Conjecture and related problems.

## Key findings

- Analysis of Waldschmidt constants and resurgences
- New bounds for bounded negativity
- Insights into symbolic power containment

## Abstract

The main focus of these notes is recent work on linear systems in which line arrangements play a role, including problems such as semi-effectivity, containment problems of symbolic powers of homogeneous ideals in their powers, bounded negativity, and a new perspective on the SHGH Conjecture. Along the way we will be concerned with asymptotic invariants such as Waldschmidt constants, resurgences and H-constants.