Resumen de Saturation and vanishing ideals

Philippe Giménez, Diego Ruano Benito, Rodrigo San José

• We consider an homogeneous ideal I in the polynomial ring S = Fq [x1, . . . ,xm] over a finite field Fq and the finite set of projective rational points X that it defines in the projective space Pm−1. We concern ourselves with the problem of computing the vanishing ideal I(X). This is usually done by adding the equations of the projective space I(Pm−1) to I and computing the radical. We give an alternative and more efficient way using the saturation with respect to the homogeneous maximal ideal.