BERNSTEIN POLYNOMIAL OF 2-PUISEUX PAIRS IRREDUCIBLE PLANE CURVE SINGULARITIES

摘要

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 1986, the second author proved the conjecture for the one Puiseux pair case. In [1], we proved the conjecture for the case in which the germ has two Puiseux pairs and its algebraic monodromy has distinct eigenvalues. In this article we aim to study the Bernstein polynomial for any function with two Puiseux pairs and its algebraic monodromy has distinct eigenvalues. In particular the set of all common roots of their corresponding Bernstein polynomials is also explicitely given. We provide also bounds for some analytic invariants of singularities and illustrate the computations in suitable examples.