Journal of Singularities
volume 8 (2014), 100-116
Received: 25 April 2014. Received in revised form: 29 September 2014.
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.
hyperplane arrangements, line arrangements, free arrangements, characteristic polynomials, exponents of arrangements
Mathematical Subject Classification:
Department of Mechanical Engineering and Science
Kyoto 606-8501, Japan