This paper presents an effective method for computing Standard bases for the local ring of an algebroid branch and for its module of Kähler differentials. This allows us to determine the semigroup of values of the ring and the values of its Kähler differentials, which in the case of complex analytic branches are, respectively, important topological and… (More)
We develop the theory of duality for projective varieties defined over fields of arbitrary characteristic. A central concept in this work is that of reflexivity and our main tool is the rank of certain local Hessians which provides a numerical criterion for reflexivity. Many of our results are necessary and sufficient conditions for reflexivity. We also… (More)
We perform the analytic classification of plane branches of multiplicity less or equal than four. This is achieved by computing a Standard basis for the modules of Kähler differentials of such branches by means of the algorithm we developed in  and then applying the classification method for plane branches presented in .