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Pseudo-automorphisms of rational threefolds and Kummer surfaces

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arxiv 2401.07948 v1 pith:OK5E6AAY submitted 2024-01-15 math.AG

classification math.AG
keywords surfaceskummerpseudo-automorphismsautomorphismsknownthreefoldadmitalong
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abstract

Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we lift $45$ classically known automorphisms of Kummer surfaces to pseudo-automorphisms of a threefold, the blow-up of $\mathbb{P}^3$ along $6$ points and $15$ lines. We give a description of a fundamental domain of the group generated by all the known pseudo-automorphisms on this threefold.

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