Abstract
Ziegler showed that the multirestriction of a free arrangement is also free. After Ziegler’s work, several results concerning the “reverse direction”, i.e., characterizing freeness of an arrangement via that of its multirestriction, have appeared. In this paper, we prove a new characterization of freeness in which the second Betti number of the arrangement plays a crucial role.
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Acknowledgments
Part of this work was done during the Workshop on Free Divisors (Warwick, June 2011) and Hyperplane arrangements and applications (Vancouver, August 2011). The authors thank organizers and participants of these conferences. Especially, the similarity of our result to formality (Remark 4.5) was pointed out by Michael Falk. Both authors are supported by JSPS Grant-in-Aid for Young Scientists (B). The authors are grateful to the referees for the careful reading and a lot of useful suggestions.
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Abe, T., Yoshinaga, M. Free arrangements and coefficients of characteristic polynomials. Math. Z. 275, 911–919 (2013). https://doi.org/10.1007/s00209-013-1165-6
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DOI: https://doi.org/10.1007/s00209-013-1165-6