Zusammenfassung für den Vortrag am 26.10.2022 (15:00 Uhr)

Seminar on Nonlinear Algebra

Marta Panizzut (MPI MiS, Leipzig)
Toric degenerations of Cox rings of blow-ups of projective \(3\)-space

We study combinatorial and geometric properties of toric degenerations of Cox rings of blow-ups of \(\mathbb{P}^3\) 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 talk is based on recent work with Mara Belotti.