Exponents of 2-multiarrangements and freeness of 3-arrangements

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.

16 pages

References in corpus (2)

• A generalized logarithmic module and duality of Coxeter multiarrangements
• An Algorithm to Construct A Basis for the Module of Logarithmic Vector Fields

Cited by in corpus (1)

• Arrangements, multiderivations, and adjoint quotient map of type ADE