Geodesic
Roots of characteristic polynomials and intersection points of line arrangements
Journal of Singularities, Tome 8 (2014), pp. 100-116

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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.
DOI : 10.5427/jsing.2014.8h
Classification : 32S22 
@article{10_5427_jsing_2014_8h,
     author = {Takuro Abe},
     title = {Roots of characteristic polynomials and intersection points of line arrangements},
     journal = {Journal of Singularities},
     pages = {100--116},
     publisher = {mathdoc},
     volume = {8},
     year = {2014},
     doi = {10.5427/jsing.2014.8h},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.8h/}
}
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Takuro Abe. Roots of characteristic polynomials and intersection points of line arrangements. Journal of Singularities, Tome 8 (2014), pp. 100-116. doi: 10.5427/jsing.2014.8h

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