English

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.

Keywords

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