The Semigroup of a Singular Point of a Curve with Two Equisingular Branches.
We investigate deformation-theoretical properties of curves carrying a half-canonical linear series of fixed dimension. In particular, we improve the previously known bound on the dimension of the corresponding loci in the moduli space and we obtain a natural description of the tangent space to higher theta loci.
Nous exprimons la multiplicité d’intersection de deux courbes se coupant au point singulier d’une surface normale en termes de valuations. C’est une généralisation du résultat connu pour les surfaces régulières.