TY - JOUR

T1 - Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations

AU - Abe, Takuro

N1 - Funding Information:
Acknowledgments . The author is grateful to Masahiko Yoshinaga for the advice of the proof of Theorem 3.2 . The author is partially supported by JSPS KAKENSHI grant number JP20K20880 .
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2022/5/15

Y1 - 2022/5/15

N2 - Terao's factorization theorem shows that if an arrangement is free, then its characteristic polynomial factors into the product of linear polynomials over the integer ring. This is not a necessary condition, for example, many integer-rooted non-free arrangements have been found in [9]. However, still main examples whose characteristic polynomials factor over the integer ring are free arrangements. On the other hand, the localization of a free arrangement is free, and its restriction is in many cases free, thus its characteristic polynomial factors. In this paper, we consider how their integer, or real roots behave.

AB - Terao's factorization theorem shows that if an arrangement is free, then its characteristic polynomial factors into the product of linear polynomials over the integer ring. This is not a necessary condition, for example, many integer-rooted non-free arrangements have been found in [9]. However, still main examples whose characteristic polynomials factor over the integer ring are free arrangements. On the other hand, the localization of a free arrangement is free, and its restriction is in many cases free, thus its characteristic polynomial factors. In this paper, we consider how their integer, or real roots behave.

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U2 - 10.1016/j.topol.2021.107990

DO - 10.1016/j.topol.2021.107990

M3 - Article

AN - SCOPUS:85122288157

SN - 0166-8641

VL - 313

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 107990

ER -