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arXiv · 1310.8260

The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold

Pierrette Cassou-Noguès·Willem Veys
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Abstract

Let I be an arbitrary ideal in C[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal Newton tree to I, related to using good coordinates in the Newton algorithm, and show that it has a conceptual geometric interpretation in terms of the log canonical model of I. We also compute the log canonical threshold from a Newton polygon and strengthen Corti's inequalities.

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Pierrette Cassou-Noguès, Willem Veys. 2013-10-30. The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold. https://arxiv.org/abs/1310.8260

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