Bernstein polynomial and value set of differentials for plane branches

2025/08/25 by Guimarães, Andrea Gomes, Hernandes, Marcelo Escudeiro
#14F10 #14H20 #32S10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17572

Abstract

In this work, we study the relation between the roots of the Bernstein polynomial \widetildeb and the value set of differentials Λ for plane branches. For plane branches defined by semiquasihomogeneous polynomial we describe the set of common roots of \widetildeb sharing by every branch with a fixed Λ set.

Citations

• From Differential Values to Roots of the Bernstein-Sato Polynomial
• On the value set of 1-forms for plane branches
• On the Analytic Invariants and Semiroots of Plane Branches
• Tjurina number of a local complete intersection curve
• Bernstein polynomial of 2-Puiseux pairs irreducible plane curve singularities
• Exponents of an irreducible plane curve singularity

Related

• Bernstein polynomial of 2-Puiseux pairs irreducible plane curve singularities
• From Differential Values to Roots of the Bernstein-Sato Polynomial
• A Method for Obtaining Polynomials of Bernstein Type of Two Variables
• On Bernstein-type theorems
• Bernstein-Sato polynomials and analytic non-equivalence of plane curve singularities