Mathematics Research Institute

Seminario de Doctorado
Seminario de Doctorado

Saturation and vanishing ideals

Rodrigo San José (Universidad de Valladolid)

Fecha: 30/06/2022 14:00
Lugar: Seminario del IMUVa, Edificio LUCIA

We consider an homogeneous ideal $I$ in the polynomial ring $S=\mathbb{F}_q[x_1,\dots,$ $x_m]$ over a finite field $\mathbb{F}_q$ and the finite set of projective rational points $\mathbb{X}$ that it defines in the projective space $\mathbb{P}^{m-1}$. We concern ourselves with the problem of computing the vanishing ideal $I(\mathbb{X})$. This is usually done by adding the equations of the projective space $I(\mathbb{P}^{m-1})$ to $I$ and computing the radical. We give an alternative and more efficient way using the saturation with respect to the homogeneous maximal ideal.