The Chow Characteristic Image of $\Spin(10)$ via the Affine Cone over the Spinor Variety

Sanghoon Baek

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arXiv · 2607.23729

The Chow Characteristic Image of $\Spin(10)$ via the Affine Cone over the Spinor Variety

Sanghoon Baek

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Abstract

Let $G=\Spin(10)$ be the split spin group over a field of characteristic different from $2$, and let $T\subset G$ be a split maximal torus. We determine the image of the integral Chow restriction map $\CH(BG)\to \CH(BT)^W$, equivalently $\CH(BG)$ modulo torsion. The main new geometric ingredient in the proof is a construction of the class $c_2c_3c_5$, where the $c_i$ are the elementary Chern classes after restriction to $T$. This class is obtained from the proper equivariant push-forward associated with the affine cone over the spinor variety in its half-spin embedding for the special Clifford group $\Gamma^+(10)$. Modulo two, the image is the subring generated, over the smallest Steenrod-stable subring of $\F[c_2,c_3,c_4,c_5]$ containing $c_2^2,c_3^2,c_4^2,c_5$ and $c_2c_3c_5$, by the torus restriction of the top Chern class of a half-spin representation. The integral characteristic image is the full inverse image of this mod-two subring under reduction modulo $2$.

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BibTeX RIS

Sanghoon Baek. 2026-07-26. The Chow Characteristic Image of $\Spin(10)$ via the Affine Cone over the Spinor Variety. https://arxiv.org/abs/2607.23729

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