Points fattening on P1×P1 and symbolic powers of bi-homogeneous ideals

We study symbolic powers of bi-homogeneous ideals of points in X=P1×P1 and extend to this setting results on the effect of points fattening obtained in [2] and [4]. We prove a Chudnovsky-type theorem for bi-homogeneous ideals and apply it to classification of configurations of points with minimal or no fattening effect.