Quadric cones on the boundary of the Mori cone for very general blowups of the plane

2023/10/16 by Ciliberto, Ciro, Miranda, Rick, Roé, Joaquim
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.10507

Abstract

We show the existence of cones over 8-dimensional rational spheres at the boundary of the Mori cone of the blow-up of the plane at s≥ 13 very general points. This gives evidence for De Fernex's strong Δ-conjecture, which is known to imply Nagata's conjecture. This also implies the existence of a multitude of good and wonderful rays as defined in Ciliberto-Harbourne-Miranda-Roé 2013.

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