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Extendability of automorphisms of K3 sur...
Matsumoto, Yuya...

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Extendability of automorphisms of K3 surfaces by Matsumoto, Yuya ( Author )
Lemonjar Open Access
Australian National University
09-08-2023
A K3 surface $X$ over a $p$-adic field $K$ is said to have good reduction if it admits a proper smooth model over the ring of integers of $K$. Assuming this, we say that a subgroup $G$ of $\mathrm{Aut}(X)$ is extendable if $X$ admits a proper smooth model equipped with $G$-action (compatible with the action on $X$). We show that $G$ is extendable if it is of finite order prime to $p$ and acts symplectically (that is, preserves the global $2$-form on $X$). The proof relies on birational geometry of models of K3 surfaces, and equivariant simultaneous resolutions of certain singularities. We also give some examples of non-extendable actions.
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Article
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30.00 KB
English
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MYR 0.01
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http://arxiv.org/abs/1611.02092
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