On the minimal value of global Tjurina numbers for line arrangements

We show that a general lower bound for the global Tjurina number of a reduced complex projective plane curve, given by Andrew A. du Plessis and Charles T. C. Wall, can be improved when the curve is a line arrangement. This fact is in sharp contrast to a conjecture saying that the general upper bound...

Full description

Saved in:
Bibliographic Details
Published inEuropean journal of mathematics Vol. 6; no. 3; pp. 817 - 828
Main Author Dimca, Alexandru
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2020
Springer Nature B.V
Springer
Subjects
Algebraic Geometry
Curves
Lower bounds
Mathematics
Mathematics and Statistics
Research Article
Upper bounds
Tjurina number
32S22
Milnor number
14H50
Line arrangement
14B05
Online AccessGet full text

Cover

More Information
Summary:We show that a general lower bound for the global Tjurina number of a reduced complex projective plane curve, given by Andrew A. du Plessis and Charles T. C. Wall, can be improved when the curve is a line arrangement. This fact is in sharp contrast to a conjecture saying that the general upper bound for the global Tjurina number of a reduced complex projective plane curve, also given by du Plessis and Wall, is realized by line arrangements in practically all cases.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-019-00373-0