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arXiv · 2304.07585

On the component group of the algebraic monodromy group of a $K3$ surface

Andreas-Stephan Elsenhans·Jörg Jahnel
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Abstract

We provide a lower bound for the number of components of the algebraic monodromy group in the situation of a $K3$ surface over a number field $k$. In the CM case, our bound is sharp. As an application, we describe, in the case of CM, the jump character \cite[Definition~2.4.6]{CEJ} entirely in terms of the endomorphism field and the geometric Picard rank.

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Andreas-Stephan Elsenhans, Jörg Jahnel. 2023-04-15. On the component group of the algebraic monodromy group of a $K3$ surface. https://arxiv.org/abs/2304.07585

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