A Note on Mustata's Computation of Multiplier Ideals of Hyperplane Arrangements

Zach Teitler

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First published in Proceedings of the American Mathematical Society in Volume 136, Number 5, May 2008, published by the American Mathematical Society.

Abstract

In 2006, M. Mustata used jet schemes to compute the multiplier ideals of reduced hyperplane arrangements. We give a simpler proof using a log resolution and generalize to non-reduced arrangements. By applying the idea of wonderful models introduced by De Concini–Procesi in 1995, we also simplify the result. Indeed, Mustat¸˘a’s result expresses the multiplier ideal as an intersection, and our result uses (generally) fewer terms in the intersection.