On the minimal value of global Tjurina numbers for line arrangements

TL;DR

This paper improves the known lower bounds for the global Tjurina number specifically for line arrangements in the complex projective plane, refining previous general results.

Contribution

It provides a tighter lower bound for the global Tjurina number in the case of line arrangements, advancing the understanding of their algebraic properties.

Findings

Improved lower bound for global Tjurina number for line arrangements

Enhanced understanding of algebraic invariants of line arrangements

Refinement of previous bounds by du Plessis and Wall

Abstract

We show that a general lower bound for the global Tjurina number of a reduced complex projective plane curve, given by A. A. du Plessis and C.T.C. Wall, can be improved when the curve is a line arrangement.