Toric degenerations of Cox rings of blow-ups of projective 3-space

Abstract:

We study combinatorial properties of toric degenerations of Cox rings of blow-ups of projective 3-space at points in general positions. We focus in particular on Ehrarht-type formulas for the multigraded Hilbert functions of these spaces. 

From our computations, it follows that the presentation ideal of the Cox ring of the blow-up of P^3 at seven points is quadratically generated, as conjectured by Lesieutre and Park. The main computational tools used are Khovanskii bases, which will be introduced in the talk. 

This is based on recent work with Mara Belotti.