Year: 2026
Type: preprint
Abstract: We study algebraic vector bundles on cluster varieties. Over a perfect field of characteristic different from two, every algebraic vector bundle is trivial on a cluster variety with principal coefficients at an acyclic seed of irreducible finite Dynkin type. The proof is based on integral contractions of cellular $\mathbb A^1$-chain complexes and successive freezing. We also construct smooth cluster varieties admitting indecomposable rank-two vector bundles, whose nontriviality is detected by quadratic Euler classes. The cellular calculation also gives a criterion for stable freeness and computes integral real cohomology and the images of cycle class maps.
Source: arXiv (Cornell University)
Authors: Liu, Haoyang, Liu, Tianle
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221524220