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arXiv · 1909.11050

Continuous automorphisms of Cremona groups

Christian Urech·Susanna Zimmermann
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Abstract

We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a similar result holds if we consider groups of polynomial automorphisms of affine spaces instead of Cremona groups.

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Christian Urech, Susanna Zimmermann. 2019-09-24. Continuous automorphisms of Cremona groups. https://arxiv.org/abs/1909.11050

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