The value semiring of an algebroid curve

The Saito module and the moduli of a germ of curve in $\left(\mathbb{C}^{2},0\right)$

“…is a constructible condition. We can now proceed analogously to prove that Γ S = Γ C is a constructible condition : indeed, according to [17], providing that Γ S ⊂ Γ C , the equality Γ S = Γ C is equivalent to the equality…”

“…Here, we overcome this issue by considering not only curves but curves enriched with a marking which allows us to recover the necessary connexity. As Ebey, we use an adapted complete topological invariant -the semi ring of values -introduced by R. Waldi [23] and some of its properties identified by M. Hernandes and Emílio de Carvalho in [17].…”