Exponents of 2-multiarrangements of three lines over fields of positive characteristic

TL;DR

This paper investigates the exponents of three-line multiarrangements over fields with positive characteristic, providing an algorithm, symmetry analysis, and examining basis constructions from binomial expansions.

Contribution

It extends the understanding of multiarrangements from characteristic zero to positive characteristic, introducing an effective computation method and symmetry insights.

Findings

Developed an algorithm for computing exponents in positive characteristic

Proved the multiplicity lattice exhibits significant symmetries

Analyzed the validity of binomial expansion-based bases in positive characteristic

Abstract

Wakamiko determined bases and the exponents for multiarrangements of three lines over a field of characteristic zero. In this paper, we study the exponents of multiarrangements of three lines for the case of positive characteristic. We provide an effective algorithm for computing the exponents. Furthermore, we prove that the multiplicity lattice has plenty of symmetries. We also discuss the validity of bases constructed from binomial expansions in the case of positive characteristic.