Toric quiver cells
Commutative Algebra
2017-07-04 v2 Algebraic Geometry
Representation Theory
Abstract
It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, B{\o}gvad's conjecture holds for quiver polytopes of dimension at most four. In arbitrary dimension, the toric ideal of a compressed polytope is generated in degree two if the polytope has no neighbouring singular vertices. Furthermore, the toric ideal of a compressed polytope with at most one singular vertex has a quadratic Gr\"obner basis.
Cite
@article{arxiv.1609.03618,
title = {Toric quiver cells},
author = {M. Domokos and Dániel Joó},
journal= {arXiv preprint arXiv:1609.03618},
year = {2017}
}