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

Author:

Ciro Ciliberto, Rick Miranda, Joaquim Roé

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-10-15 16:00:00

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 $s\geq 13$ very general points. This gives evidence for De Fernex's strong $\Delta$-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-Ro\'e 2013.

PDF: Quadric cones on the boundary of the Mori cone for very general blowups of the plane.pdf