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SUMMARY:Quotients of higher dimensional Cremona groups - Jérémy Blanc (B
 asel)
DTSTART:20190515T131500Z
DTEND:20190515T141500Z
UID:TALK118528@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:We study large groups of birational transformations $\\mathrm{
 Bir}(X)$\, where $X$ is a variety of dimension at least $3$\, defined over
  $\\mathbb{C}$ or a subfield of $\\mathbb{C}$.\nTwo prominent cases are wh
 en $X$ is the projective space $\\mathbb{P}^n$\, in which case $\\Bir(X)$ 
 is the Cremona group of rank~$n$\, or when $X \\subset \\mathbb{P}^{n+1}$ 
 is a smooth cubic hypersurface.\nIn both cases\, and more generally when $
 X$ is birational to a conic bundle\, we produce infinitely many distinct g
 roup homomorphisms from $\\mathrm{Bir}(X)$ to $\\mathbb{Z}/2$.\nAs a conse
 quence we also obtain that the Cremona group of rank~$n \\ge 3$ is not gen
 erated by linear and Jonquières elements.\nJoint work with Stéphane Lamy
  and Susanna Zimmermann\n
LOCATION:CMS MR13
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