Seminar Algebra and Geometry: Christian Urech (EPFL)

On continuous automorphisms of Cremona groups

Julie Déserti showed that every automorphism of the plane Cremona group is inner up to a field automorphism of the base-field. In this talk we generalize this result to Cremona groups of arbitrary rank, however, only under the additional restriction that the automorphisms are also homeomorphisms with respect to the Zariski or the Euclidean topology on the Cremona group. We will consider similar questions for groups of polynomial automorphisms and groups of birational diffeomorphisms. This is joint work with Susanna Zimmermann.

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