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SUMMARY:Recursively patchworking real algebraic hypersurfaces with asympto
 tically large Betti numbers - Charles Arnal\, INRIA
DTSTART:20230524T131500Z
DTEND:20230524T141500Z
UID:TALK199402@talks.cam.ac.uk
CONTACT:Mark Gross
DESCRIPTION:Understanding the possible topologies of real projective algeb
 raic\nhypersurfaces in a given degree and dimension is a key problem in re
 al\nalgebraic geometry\, and can be seen as a natural generalization of Hi
 lbert's\n16th problem.\nThere are two complementary approaches to this pro
 blem : searching for new\nconstraints\, and conversely building examples t
 o show that the configurations\nwhich we could not rule out are in fact re
 alizable.\nI will present a new technique that builds on previous work by 
 O. Viro and I.\nItenberg and allows one to effortlessly define families of
  real projective\nalgebraic hypersurfaces using already-defined families i
 n lower dimensions as\nbuilding blocks. The asymptotic (in the degree) Bet
 ti numbers of the real parts\nof the resulting families can then be recove
 red from the asymptotic Betti\nnumbers of the real parts of the building b
 locks.\nUsing this technique\, I will explain how families of real algebra
 ic\nhypersurfaces whose real parts have asymptotically large Betti numbers
  can be\nconstructed in any dimension.\nThe results presented in this talk
  can also be found in\nhttps://londmathsoc.onlinelibrary.wiley.com/doi/10.
 1112/topo.12251.
LOCATION:CMS MR13
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