Higher rank Gelfand-Kapranov-Zelevinsky fans
Algebraic Geometry
2026-04-23 v1 Commutative Algebra
Combinatorics
Abstract
We define and study the higher rank GKZ-fans of point configurations, where the rank one cases coincide with the usual GKZ-fans. A point in a higher rank GKZ-fan is then used to construct higher rank quasi-valuations to degenerate the toric variety associated to the point configuration flatly to a reduced union of toric varieties. Such a union encodes the polytopal subdivision arising from the point in the higher rank GKZ-fan.
Cite
@article{arxiv.2604.20250,
title = {Higher rank Gelfand-Kapranov-Zelevinsky fans},
author = {Rocco Chirivì and Martina Costa Cesari and Xin Fang and Peter Littelmann},
journal= {arXiv preprint arXiv:2604.20250},
year = {2026}
}
Comments
43 pages, comments are welcome