Higher rank Gelfand-Kapranov-Zelevinsky fans
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.
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