Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Heavy Hyperplanes in Multiarrangements   Hyperplane Arrangements of rank $3$ admitting an unbalanced Ziegler
restriction are known to fulfill Terao's conjecture. This long-standing
conjecture asks whether the freeness of an arrangement is determined by its
combinatorics. In this note, we prove that arrangements that admit a locally
heavy flag satisfy Terao's conjecture which is a generalization of the
statement above to arbitrary dimension. To this end, we extend results
characterizing the freeness of multiarrangements with a heavy hyperplane to
those satisfying the weaker notion of a locally heavy hyperplane. As a
corollary, we give a new proof that irreducible arrangements with a generic
hyperplane are totally non-free. In another application, we show that an
irreducible multiarrangement of rank $3$ with at least two locally heavy
hyperplanes is not free.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: econ