Symbolic powers of planar point configurations II

TL;DR

This paper investigates the initial sequences of planar point configurations, extends previous work to asymptotic Waldschmidt constants, and introduces the Bezout Decomposition concept, providing new insights into symbolic powers.

Contribution

It advances the understanding of symbolic powers of planar points by answering prior questions and introducing the novel Bezout Decomposition method.

Findings

Resolved several open questions from previous work.

Extended analysis to asymptotic Waldschmidt constants.

Introduced the Bezout Decomposition concept.

Abstract

We study initial sequences of various configurations of planar points. We answer several questions asked in our previous paper (Symbolic powers of planar point configurations), and we extend our considerations to the asymptotic setting of Waldschmidt constants. We introduce the concept of Bezout Decomposition which might be of independent interest.