On the Hilbert function of general fat points in ${\mathbb{P}}^1\times {\mathbb{P}}^1$

Enrico Carlini, Maria Virginia Catalisano, Alessandro Oneto

We study the bi-graded Hilbert function of ideals of general fat points with same multiplicity in ${\mathbb{P}}^1\times {\mathbb{P}}^1$. Our first tool is the multiprojective-affine-pro…