English

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

Algebraic Geometry 2025-05-08 v1 Algebraic Topology

Abstract

In this paper, we present the calculations of cellular A1\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.

Keywords

Cite

@article{arxiv.2505.04520,
  title  = {Cellular $\mathbb{A}^1$-Homology of Smooth Toric Varieties},
  author = {Haoyang Liu and Keyao Peng},
  journal= {arXiv preprint arXiv:2505.04520},
  year   = {2025}
}