Computing Hironaka's invariants: Ridge and Directrix

Jérémy Berthomieu (1) , Pascal Hivert (2) , Hussein Mourtada (2)

1 Équipe Max
2 Équipe Algèbre et Géométrie

In this note we present Hironaka's invariants as developed by Giraud: the ridge and the directrix. We give an effective definition and a functorial one and show their equivalence. The fruit is an effective algorithm that computes the additive generators of the "ridge", and the generators of its invariant algebra.

Mots clés: resolution of singularities; invariants; Algebraic geometry

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]; Calcul formel [cs.SC]

Jérémy Berthomieu, Pascal Hivert, Hussein Mourtada. Computing Hironaka's invariants: Ridge and Directrix. Papers from the 12th Conference (AGC2T 12) held in Marseille, March 30--April 3, 2009, the 1st Geocrypt Conference held in Pointe-à-Pitre, April 27-May 1, 2009, and the European Science Foundation Exploratory Workshop on Curves, Coding Theory and Cryptography held in Marseille, March 25-29, 2009., Mar 2009, Marseille, France. pp.12, ⟨10.1090/conm/521⟩. ⟨hal-00492824⟩