Birational Maps of Severi-Brauer Surfaces, with Applications to Cremona Groups of Higher Rank

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• Julia Schneider, Universität Zürich
• Wednesday 28 February 2024, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Holly Krieger.

We describe the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field, proving that if it contains a point of degree 6, then it is not generated by elements of finite order. We then use this result to study Mori fibre spaces over the field of complex numbers and deduce that the Cremona group of rank at least 4 admits any group (of cardinality at most $|\mathbb{C}|$) as a quotient. Moreover, we prove that the 3-torsion in the abelianization of the Cremona group of rank at least 4 is uncountable. This is based on a joint work with J. Blanc and E. Yasinsky.

This talk is part of the Algebraic Geometry Seminar series.

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