Higher rank Gelfand-Kapranov-Zelevinsky fans
Rocco Chiriv\`i, Martina Costa Cesari, Xin Fang, Peter Littelmann
TL;DR
This paper introduces higher rank GKZ-fans for point configurations, extending the classical GKZ-fans, and uses them to construct degenerations of toric varieties via higher rank quasi-valuations.
Contribution
It defines higher rank GKZ-fans and demonstrates their role in constructing degenerations of toric varieties through higher rank quasi-valuations.
Findings
Higher rank GKZ-fans generalize classical GKZ-fans.
They encode polytopal subdivisions of point configurations.
They enable flat degenerations of toric varieties to unions of toric varieties.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.