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arXiv · 2605.04347

Smoothing low-dimensional cycles in algebraic cobordism

Chuhao Huang
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Abstract

We show that every cycle in the degree $d$ algebraic cobordism group $\Omega_d(X)$ of a smooth projective variety $X$ over a field of characteristic $0$ is smoothable when $2d<\dim(X)$, that is, it can be written as a linear combination of cycles represented by smooth closed subvarieties of $X$. This generalizes a result of Koll\'ar and Voisin from Chow groups to algebraic cobordism groups.

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Chuhao Huang. 2026-05-05. Smoothing low-dimensional cycles in algebraic cobordism. https://arxiv.org/abs/2605.04347

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