Roots of characteristic polynomials and intersection points of line arrangements
Combinatorics
2014-04-17 v3 Algebraic Geometry
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-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.
Keywords
Cite
@article{arxiv.1302.3822,
title = {Roots of characteristic polynomials and intersection points of line arrangements},
author = {Takuro Abe},
journal= {arXiv preprint arXiv:1302.3822},
year = {2014}
}
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