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Quotients of higher dimensional Cremona groups

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01981369
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Submitted on : Tuesday, January 15, 2019 - 8:28:11 AM
Last modification on : Tuesday, April 5, 2022 - 3:40:42 AM

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

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