Exponents of 2-multiarrangements and freeness of 3-arrangements

Details Exponents of 2-multiarrangements and freeness of 3-arrangements Exponents of 2-multiarrangements and freeness of 3-arrangements

2010-05-28

arxiv.org/abs/1005.5276v1

Mathematics

Commutative Algebra

16 pages

Scientific paper

We give the upper bound of differences of exponents for balanced
2-multiarrangements in terms of the cardinality of hyperplanes. Also, we give a
shift isomorphism of 2-multiarrangements like Coxeter arrangements when the
difference of exponents is maximum. As an application, a sufficient numerical
and combinatorial condition for 3-arrangements to be free is given.

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