Exponents of 2-multiarrangements and freeness of 3-arrangements
classification
🧮 math.AC
math.AG
keywords
arrangementsexponentsmultiarrangementsgiveapplicationbalancedboundcardinality
read the original abstract
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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