## Navid Nemati - Complete intersection points in product of projective spaces

24 March 2020 –

**Complete intersection points in product of projective spaces**

**Navid Nemati**

I will report on ongoing project with Marc Chardin. we study the bigraded Hilbert function of complete intersection sets of points in $\mathbb{P}^n \times \mathbb{P}^m$. We give a sharp lower bound for the stabilization of the bigraded Hilbert function. In addition, we show that, in a specific and pretty large region, the bigraded Hilbert Function only depends upon the degree of the forms defining the points. Finally, we consider the case where the forms defining the points are chosen generically. In this case we show that the natural projections to $\mathbb{P}^n$ and $\mathbb{P}^m$ are one-to-one.