On the value set of 1-forms for plane branches

2021/05/26 by de Abreu, Marcelo Osnar Rodrigues, Hernandes, Marcelo Escudeiro · 1 citation
#14H20 #32S10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.12575

Abstract

The value semigroup Γ and the value set Λ of 1-forms are, respectively, a topological and an analytical invariant of a plane branch. Giving a plane branch C with semigroup Γ there are a finitely number of distinct possible sets Λ_i according to the analytic class of C. In this work we show that the value set of 1-forms Λ determines the semigroup Γ and we present an effective method to recover Γ by Λ. In particular, this allows us to decide if a subset of ℕ is a value set of 1-forms for a plane branch.

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• Bernstein polynomial and value set of differentials for plane branches

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