Discrete geometry of Cox rings of blow-ups of ℙ³
Abstract
We prove quadratic generation for the ideal of the Cox ring of the blow-up of P 3 \mathbb {P}^3 at 7 7 points, solving a conjecture of Lesieutre and Park. To do this we compute Khovanskii bases, implementing techniques which proved successful in the case of del Pezzo surfaces. Such bases give us degenerations to toric varieties whose associated polytopes encode toric degenerations with respect to all projective embeddings. We study the edge-graphs of these polytopes and we introduce the Mukai edge graph .
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Polynomial and algebraic computation
Publication details
- Journal / source
- Mathematics of Computation
- Volume
- 95
- Issue
- 362
- Pages
- 3081–3100
- Publication date
- 27 January 2026
- Language
- EN