Singular loci of reflection arrangements and the containment problem

Abstract

This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci of hyperplane arrangements in projective space, with emphasis on arrangements arising from complex reflection groups. We provide minimal sets of equations for the radical ideals defining these singular loci and study containments between the ordinary and symbolic powers of these ideals.

arXiv commentMinor revision: proof of Proposition 6.3 corrected. To appear in Mathematische Zeitschrift

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Cited by in corpus (2)

• A stable version of Harbourne's Conjecture and the containment problem for space monomial curves
• Symbolic Rees algebras