Yano's Conjecture for Two-Puiseux-Pairs irreducible Plane Curve Singularities

Enrique Artal Bartolo , Pierrette Cassou-Noguès (1) , Ignacio Luengo Velasco (2) , Alejandro Melle Hernandez (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 Departamento de Algebra [Madrid]
3 Departamento de Algebra [Madrid]

In 1982, Tamaki Yano proposed a conjecture predicting the b- exponents of an irreducible plane curve singularity germ which is generic in its equisingularity class. In this article we prove the conjecture for the case in which the irreducible germ has two Puiseux pairs and its algebraic monodromy has distinct eigenvalues. This hypothesis on the monodromy implies that the b-exponents coincide with the opposite of the roots of the Bernstein polynomial, and we compute the roots of the Bernstein polynomial.

Mots clés: Bernstein polynomial; b-exponents; improper integrals.

Domaines: Géométrie algébrique [math.AG]

Enrique Artal Bartolo, Pierrette Cassou-Noguès, Ignacio Luengo Velasco, Alejandro Melle Hernandez. Yano's Conjecture for Two-Puiseux-Pairs irreducible Plane Curve Singularities. Publications of the Research Institute for Mathematical Sciences, 2017, 53. ⟨hal-01447426⟩