Cellular \mathbbA¹-Homology of Smooth Toric Varieties

2025/05/07 by Haoyang Liu, Liu, Haoyang, Keyao Peng +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2505.04520

Abstract

In this paper, we present the calculations of cellular \mathbbA¹-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.

Citations

• Polyhedral products in abstract and motivic homotopy theory
• Cohomology rings of quasitoric bundles
• Milnor-Witt Motives
• Geometric representations of finite groups on real toric spaces
• Motivic and real étale stable homotopy theory
• Integral cohomology groups of real toric manifolds and small covers
• Wonderful models of subspace arrangements

Related

• Cellular \mathbb A¹-homology and the motivic version of Matsumoto's theorem
• Oriented Borel-Moore homologies of toric varieties
• On torsion in homology of singular toric varieties
• Toric chordality
• A Resolution of the Diagonal for Smooth Projective Toric Varieties