CONTINUOUS AUTOMORPHISMS OF CREMONA GROUPS

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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https://hal.archives-ouvertes.fr/hal-02302583
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Submitted on : Tuesday, October 1, 2019 - 4:47:42 PM
Last modification on : Monday, October 14, 2019 - 10:34:48 AM

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Christian Urech, Susanna Zimmermann. CONTINUOUS AUTOMORPHISMS OF CREMONA GROUPS. 2019. ⟨hal-02302583⟩

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