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Plus-one generated and next to free arrangements of hyperplanes

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arxiv 1808.04697 v3 pith:P5MUPTY2 submitted 2018-08-14 math.AC math.AGmath.CO

classification math.ACmath.AGmath.CO
keywords arrangementsplus-onegeneratedfreestrictlyfreenessgeneratednesshyperplanes
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We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freeness, i.e., plus-one generated arrangements have their logarithmic derivation modules generated by dimension plus one elements, with relations containing one linear form coefficient. We show that strictly plus-one generated arrangements can be obtained if we delete a hyperplane from free arrangements. We show a relative freeness criterion in terms of plus-one generatedness. In particular, for plane arrangements, we show that a free arrangement is in fact surrounded by free or strictly plus-one generated arrangements. We also give several applications.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Combinatorially Determined Zeroes of Bernstein--Sato Ideals for Tame and Free Arrangements

    math.AG 2019-09 accept novelty 7.0 of 10

    For tame and free hyperplane arrangements, the zero loci of Bernstein-Sato ideals and the roots in [-1,0) of Bernstein-Sato polynomials are determined by the intersection lattice, with explicit combinatorial formulas.

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