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In contrast to the Milnor number, there was no known formula relating the Tjurina number of a reducible curve to the Tjurina numbers of its components. In this work we exhibit such a formula relating Tjurina number of a complete intersection algebroid (or analytic) curve over an algebraically closed field of characteristic zero (or over C ) to the Tjurina numbers of its components, involving the intersection indices among the components and numerical analytic invariants extracted from modules of Kähler differentials on unions of branches of the curve. [ABSTRACT FROM AUTHOR] more...

In this paper, we present a solution to the problem of the analytic classification of germs of plane curves with several irreducible components. Our algebraic approach follows precursive ideas of Oscar Zariski and as a subproduct allows us to recover some particular cases found in the literature. [ABSTRACT FROM AUTHOR] more...

In this paper, we introduce a distinguished expression for a given 1-form with respect to a polynomial f ∈ ℂ { x } [ y ] , called Weierstrass form. We will use this form and the properties of plane analytical curves to give new characterizations of nondicritical generalized curve foliations. [ABSTRACT FROM AUTHOR] more...

The value semigroup Γ and the value set Λ of 1-forms are, respectively, a topological and an analytical invariant of a plane branch. Given a plane branch C with value semigroup Γ there are a finitely number of distinct possible sets Λ according to the analytic class of C . In this work we show that the value set of 1-forms Λ determines the value 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. [ABSTRACT FROM AUTHOR] more...