Roots of characteristic polynomials and intersection points of line arrangements

Abstract

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.

18 pages (ver.1). 20 pages (ver. 2). Example 1.4 (1) and Theorem 1.6 are added. 18 pages (ver. 3). Section 7 is added

References in corpus (4)

• Logarithmic bundles and Line arrangements, an approach via the standard construction
• Freeness of hyperplane arrangements and related topics
• Exponents of 2-multiarrangements and freeness of 3-arrangements
• Free but not recursively free arrangements

Cited by in corpus (2)

• Non-recursive freeness and non-rigidity of plane arrangements
• The smallest line arrangement which is free but not recursively free