Roots of characteristic polynomials and intersection points of line arrangements

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

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