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

Pierrette Cassou-Noguès, Willem Veys
2013 arXiv   pre-print
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.
arXiv:1310.8260v1 fatcat:kkbfwo5xrzglrkp3gkhfvkmsjm