2022/08/10 by Mara Belotti, Belotti, Mara, Marta Panizzut +1
Computer Science · Mathematics · #14D06 #14M25 #14Q15 #52B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2208.05258
openalex publication_date 2022/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove quadratic generation for the ideal of the Cox ring of the blow-up of ℙ3 at 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.