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

  • Marta Panizzut (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)


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.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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