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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
Contributor : Stéphane Lamy <>
Submitted on : Tuesday, January 15, 2019 - 8:28:11 AM
Last modification on : Tuesday, March 10, 2020 - 1:32:50 AM

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  • HAL Id : hal-01981369, version 1
  • ARXIV : 1901.04145

Citation

Jérémy Blanc, Stéphane Lamy, Susanna Zimmermann. Quotients of higher dimensional Cremona groups. 2019. ⟨hal-01981369⟩

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