Initial sequences and Waldschmidt constants of planar point configurations

TL;DR

This paper extends the classification of planar point configurations with low Waldschmidt constants below 2.5 and proves a related conjecture about initial sequences with low first differences.

Contribution

It provides a comprehensive classification for configurations with low Waldschmidt constants and confirms a conjecture on initial sequences, advancing understanding in algebraic geometry.

Findings

Classification of planar point configurations with Waldschmidt constants less than 2.5

Proof of a conjecture on initial sequences with low first differences

Enhanced understanding of algebraic properties of point configurations

Abstract

The purpose of this work is to extend the classification of planar point configurations with low Waldschmidt constants for all values less than $5/2$. As a consequence we prove a conjecture of Dumnicki, Szemberg and Tutaj-Gasi\'nska concerning initial sequences with low first differences.