39 citations · 55 across the 13 of their papers we have counts for
15 papers
Decorated trees
Pierrette Cassou-Noguès, Daniel Daigle
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each o…
Milnor number of plane curve singularities in arbitrary characteristic
Enrique Artal Bartolo, Pierrette Cassou-Noguès
Reduced power series in two variables with coefficients in a field of characteristic zero satisfy a well-known formula that relates a codimension related to the normalization of a…
Local motivic invariants of rational functions in two variables
Pierrette Cassou-Noguès, Michel Raibaut
Let and be two polynomials in two variables with coefficients in an algebraic closed field of characteristic zero. We consider the rational function . For an indeter…
Newton transformations and motivic invariants at infinity of plane curves
Pierrette Cassou-Noguès, Michel Raibaut
In this article we give an expression of the motivic Milnor fiber at infinity and the motivic nearby cycles at infinity of a polynomial in two variables with coefficients in an…
Field generators in two variables and birational endomorphisms of
Pierrette Cassou-Noguès, Daniel Daigle
This article is a survey of two subjects: the first part is devoted to field generators in two variables, and the second to birational endomorphisms of the affine plane. Each one o…
Structure of the Newton tree at infinity of a polynomial in two variables
Pierrette Cassou-Nogues, Daniel Daigle
Let be a polynomial map. Let be a compactification of where is a smooth rational compact surface and suc…
Rational polynomials of simple type: a combinatorial proof
Pierrette Cassou-Noguès, Daniel Daigle
We determine the Newton trees of the rational polynomials of simple type, thus filling a gap in the proof of the classification of these polynomials given by Neumann and Norbury.
Bernstein polynomial of 2-Puiseux pairs irreducible plane curve singularities
E. Artal Bartolo, Pi. Cassou-Noguès, I. Luengo +1
In 1982, Tamaki Yano proposed a conjecture predicting the set of b-exponents of an irreducible plane curve singularity germ which is generic in its equisingularity class. In \cite{…
The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold
Pierrette Cassou-Noguès, Willem Veys
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 face…
Very good and very bad field generators
Pierrette Cassou-Noguès, Daniel Daigle
Let k be a field. A "field generator" is a polynomial F in k[X,Y] satisfying k(F,G) = k(X,Y) for some G in k(X,Y). If G can be chosen in k[X,Y], we call F a "good field generator";…
Compositions of birational endomorphisms of the affine plane
Pierrette Cassou-Noguès, Daniel Daigle
Let A^2 denote the affine plane over an algebraically closed field of arbitrary characteristic. Besides contributing several new results in the general theory of birational endomor…
Invariants of plane curve singularities and Newton diagrams
Pierrette Cassou-Noguès, Arkadiusz Płoski
We present an intersection-theoretical approach to the invariants of plane curve singularities , , related by the Milnor formula . Using Newton transformations…
Newton trees for ideals in two variables and applications
Pierrette Cassou-Noguès, Willem Veys
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algor…
Multivariable Hodge theoretical invariants of germs of plane curves
Pierrette Cassou-Nogues, Anatoly Libgober
We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of mul…
Quasi-ordinary power series and their zeta functions
E. Artal Bartolo, Pi. Cassou-Noguès, I. Luengo +1
The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number…