Fitting ideals and multiple-points of surface parameterizations

Nicolás Botbol (1) , Laurent Busé (2) , Marc Chardin (3, 4)

1 Departamento de Matemática [Buenos Aires]
2 GALAAD - Geometry, algebra, algorithms
3 IMJ - Institut de Mathématiques de Jussieu
4 UPMC - Université Pierre et Marie Curie - Paris 6

Given a birational parameterization of an algebraic surface S in the projective space, the purpose of this paper is to investigate the sets of points on S whose preimage consists in k or more points, counting multiplicities. They are described explicitly in terms of Fitting ideals of some graded parts of the symmetric algebra associated to this parameterization.

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]; Calcul formel [cs.SC]

Nicolás Botbol, Laurent Busé, Marc Chardin. Fitting ideals and multiple-points of surface parameterizations. 2013. ⟨hal-00874221v1⟩