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arXiv · 2604.20250

Higher rank Gelfand-Kapranov-Zelevinsky fans

Rocco Chirivì·Martina Costa Cesari·Xin Fang·Peter Littelmann
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Abstract

We define and study the higher rank GKZ-fans of point configurations, serving as the set of discrete and homogeneous quasi-valuations on the homogeneous coordinate ring of the associated toric variety, where the rank one cases coincide with the usual GKZ-fans. Such a quasi-valuation is then used to degenerate the toric variety flatly to a reduced union of toric varieties, which encodes the polytopal subdivision arising from the point in the higher rank GKZ-fan.

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Rocco Chirivì, Martina Costa Cesari, Xin Fang, Peter Littelmann. 2026-09-13. Higher rank Gelfand-Kapranov-Zelevinsky fans. https://arxiv.org/abs/2604.20250

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