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arXiv · 2505.04520

Cellular $\mathbb{A}^1$-Homology of Smooth Toric Varieties

Haoyang Liu·Keyao Peng
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Abstract

In this paper, we present the calculations of cellular $\mathbb{A}^1$-homology for smooth toric varieties, along with an explicit description of pure shellable cases. Consequently, we derive the (Milnor-Witt) motivic decomposition for these pure shellable cases. Furthermore, we obtain an additive basis for the Chow groups of general smooth toric varieties.

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Haoyang Liu, Keyao Peng. 2025-05-07. Cellular $\mathbb{A}^1$-Homology of Smooth Toric Varieties. https://arxiv.org/abs/2505.04520

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