Sagbi Bases of Cox-Nagata Rings
Algebraic Geometry
2008-03-11 v2 Combinatorics
Abstract
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 establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D'Cruz-Iarobbino and Buczynska-Wisniewski. Inspired by the zonotopal algebras of Holtz and Ron, our study emphasizes explicit computations, and offers a new approach to Hilbert functions of fat points.
Cite
@article{arxiv.0803.0892,
title = {Sagbi Bases of Cox-Nagata Rings},
author = {Bernd Sturmfels and Zhiqiang Xu},
journal= {arXiv preprint arXiv:0803.0892},
year = {2008}
}
Comments
35 pages. Results in Section 7 improved