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arXiv:1302.3822 [math.CO]AbstractReferencesReviewsResources

Roots of characteristic polynomials and intersection points of line arrangements

Takuro Abe

Published 2013-02-15, updated 2014-04-16Version 3

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-Vall\`{e}s' 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.

Comments: 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
Categories: math.CO, math.AG
Subjects: 32S22
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