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arXiv · 2606.13907

Nonsimplicial toric Nullstellensatz and stacky GKZ theory

Christine Berkesch·Daniel Erman·David Favero
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Abstract

We introduce a variant of the Cox ring using $\mathbb{Q}$-Cartier divisors and use this to remedy various deficiencies of nonsimplicial toric varieties. Our main applications are: Cox's ideal-variety correspondence, an explicit classification of subschemes and sheaves in terms of multigraded modules, an associated toric Deligne-Mumford stack, and a stacky extension of the GKZ/Mori theory of toric varieties.

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Christine Berkesch, Daniel Erman, David Favero. 2026-06-11. Nonsimplicial toric Nullstellensatz and stacky GKZ theory. https://arxiv.org/abs/2606.13907

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