Exponents of 2-multiarrangements and multiplicity lattices

TL;DR

This paper introduces the concept of multiplicity lattices for 2-multiarrangements, explores their combinatorial and geometric properties, and provides methods to construct bases for derivation modules efficiently.

Contribution

It presents a new framework for understanding 2-multiarrangements through multiplicity lattices and offers practical tools for basis construction.

Findings

Characterization of multiplicity lattices' structure

Criteria for basis construction of derivation modules

Effective methods for basis construction

Abstract

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.