The Euler multiplicity and addition�deletion theorems for multiarrangements

• Autores: Takuro Abe, Hiroaki Terao, Max Wakefield
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 2, 2008, págs. 335-348
• Idioma: inglés
• DOI: 10.1112/jlms/jdm110
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• Resumen

  • The addition�deletion theorems for hyperplane arrangements, which were originally shown by Terao [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980) 293�320.], provide useful ways to construct examples of free arrangements. In this article, we prove addition�deletion theorems for multiarrangements. A key to the generalization is the definition of a new multiplicity, called the Euler multiplicity, of a restricted multiarrangement. We compute the Euler multiplicities in many cases. Then we apply the addition�deletion theorems to various arrangements, including supersolvable arrangements and the Coxeter arrangement of type A3, to construct free and non-free multiarrangements.