Roots of characteristic polynomials and intersection points of line arrangements

Takuro Abe

Journal of Singularities
volume 8 (2014), 100-116

Received: 25 April 2014. Received in revised form: 29 September 2014.

DOI: 10.5427/jsing.2014.8h

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Abstract:

We study a relation between roots of characteristic polynomials and intersection points of line arrangements. Using these results, we obtain many applications for line arrangements. Namely, we give (i) a generalized addition theorem for line arrangements, (ii) a generalization of Faenzi-Vallès' freeness criterion related to a certain multiple intersection point, (iii) a partial result on the conjecture of Terao for line arrangements, and (iv) a new sufficient condition for freeness over finite fields. Also, a higher-dimensional version of our main results is considered.

Keywords:

hyperplane arrangements, line arrangements, free arrangements, characteristic polynomials, exponents of arrangements

Mathematical Subject Classification:

Primary 32S22

Author(s) information:

Takuro Abe
Department of Mechanical Engineering and Science
Kyoto University
Kyoto 606-8501, Japan
email: abe.takuro.4c@kyoto-u.ac.jp