A note on Mather-Jacobian multiplier ideals

Wenbo Niu; Bernd Ulrich

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arXiv · 1404.5092

A note on Mather-Jacobian multiplier ideals

Wenbo Niu·Bernd Ulrich

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Abstract

By using Mather-Jacobian multiplier ideals, we first prove a formula on comparing Grauert-Riemenschneider canonical sheaf with canonical sheaf of a variety over an algebraically closed field of characteristic zero. Then we turn to study Mather-Jacobian multiplier ideals on algebraic curve, in which case the definition of Mather-Jacobian multiplier ideal can be extended to a ground field of any characteristic. We show that Mather-Jacobian multiplier ideal on curves is essentially the same as an integrally closed ideal. Finally by comparing conductor ideal with Mather-Jacobian multiplier ideal, we give a criterion when an algebraic curve is a locally complete intersection.

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Wenbo Niu, Bernd Ulrich. 2014-04-21. A note on Mather-Jacobian multiplier ideals. https://arxiv.org/abs/1404.5092

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