2017/04/17 by Emilio Carvalho, Carvalho, Emilio, Marcelo Escudeiro Hernandes +1
Computer Science · Mathematics · #14H20 #14H50 #14Q05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1704.04948
openalex publication_date 2017/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the semiring of values Γ with respect to the tropical operations associated to an algebroid curve. As a set, Γ determines and is determined by the well known semigroup of values S and we prove that Γ is always finitely generated in contrast to S. In particular, for a plane curve, we present a straightforward way to obtain Γ in terms of the semiring of each branch of the curve and the mutual intersection multiplicity of its branches. In the analytical case, this allows us to connect directly the results of Zariski and Waldi that characterize the topological type of the curve.