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arXiv · 2504.04328

Clifford Multiplication on Spinor Abelian Varieties

Ivona Grzegorczyk·Ricardo Suarez
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Abstract

We define a spinor Abelian variety $S_{\Delta}$ to be a complex Abelian variety whose tangent space at the origin is a space of spinors for a suitable complex Clifford algebra $\mathbb{C}_{q}(V)$. We examine intrinsic properties of such varieties and the connection between Clifford multiplication and their endomorphism algebras. We then extend the analysis of Clifford multiplication to the dual torus $Pic^{0}(S_{\Delta})$.

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Ivona Grzegorczyk, Ricardo Suarez. 2025-04-06. Clifford Multiplication on Spinor Abelian Varieties. https://arxiv.org/abs/2504.04328

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