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Article Dans Une Revue Acta Mathematica Année : 2021

Quotients of higher dimensional Cremona groups

Résumé

We study large groups of birational transformations Bir(X), where X is a variety of dimension at least 3, defined over C or a subfield of C. Two prominent cases are when X is the projective space, in which case Bir(X) is the Cremona group of rank n, or when X is a smooth cubic hypersurface. In both cases, and more generally when X is birational to a conic bundle, we produce infinitely many distinct group homomorphisms from Bir(X) to Z/2. As a consequence we also obtain that the Cremona group of rank n at least 3 is not generated by linear and Jonqui\`eres elements.

Dates et versions

hal-01981369 , version 1 (15-01-2019)

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Jérémy Blanc, Stéphane Lamy, Susanna Zimmermann. Quotients of higher dimensional Cremona groups. Acta Mathematica, 2021, ⟨10.4310/ACTA.2021.v226.n2.a1⟩. ⟨hal-01981369⟩
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