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arXiv · 2504.08270

Kuga-Satake construction on families of K3 surfaces of Picard rank 14

Flora Poon
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Abstract

The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised abelian $8$-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga-Satake construction. Furthermore, we illustrate how the the modular mapping can be realised for any specific families of K3 surfaces of Picard rank $14$, which can be specialised to families of K3 surfaces of higher Picard rank.

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Flora Poon. 2025-04-11. Kuga-Satake construction on families of K3 surfaces of Picard rank 14. https://arxiv.org/abs/2504.08270

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