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Continuous automorphisms of Cremona groups (1909.11050v1)
Published 24 Sep 2019 in math.AG and math.GR
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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