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Sagbi bases of Cox-Nagata rings
We degenerate Cox-Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev-Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective $n$-space at $n+3$ points, sagbi bases of Cox-Nagata rings are related to phylogenetic algebraic geometry. This computational study was inspired by the zonotopal algebras of Holtz and Ron, and offers a new approach to Hilbert functions of fat points.
Reference: arXiv:0803.0892v1
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