Sagbi bases of Cox–Nagata rings

Sturmfels, Bernd, and Xu, Zhiqiang. "Sagbi bases of Cox–Nagata rings." Journal of the European Mathematical Society 012.2 (2010): 429-459. <http://eudml.org/doc/277625>.

@article{Sturmfels2010,
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–Iarrobino and Buczyńska–Wiśniewski. 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.},
author = {Sturmfels, Bernd, Xu, Zhiqiang},
journal = {Journal of the European Mathematical Society},
keywords = {Cox ring; del Pezzo surface; phylogenetic variety; fat points; Sagbi basis; Nagata action; Cox ring; del Pezzo surface; phylogenetic variety; fat points; Sagbi basis; Nagata action},
language = {eng},
number = {2},
pages = {429-459},
publisher = {European Mathematical Society Publishing House},
title = {Sagbi bases of Cox–Nagata rings},
url = {http://eudml.org/doc/277625},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Sturmfels, Bernd
AU - Xu, Zhiqiang
TI - Sagbi bases of Cox–Nagata rings
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 2
SP - 429
EP - 459
AB - 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–Iarrobino and Buczyńska–Wiśniewski. 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.
LA - eng
KW - Cox ring; del Pezzo surface; phylogenetic variety; fat points; Sagbi basis; Nagata action; Cox ring; del Pezzo surface; phylogenetic variety; fat points; Sagbi basis; Nagata action
UR - http://eudml.org/doc/277625
ER -