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UID:7840@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160418T100000
DTEND;TZID=Europe/Paris:20160418T110000
DTSTAMP:20241120T205550Z
URL:https://www.i2m.univ-amu.fr/evenements/recouvrements-doublants-d-hyper
 surfaces-algebriques/
SUMMARY:Omer Friedland (IMJ-PRG\, Sorbonne Université\, Paris): Recouvreme
 nts doublants d'hypersurfaces algébriques
DESCRIPTION:Omer Friedland: Doubling coverings of algebraic hypersurfaces\n
 A doubling covering $\\U$ of a complex $n$-dimensional manifold $Y$ consis
 ts of analytic charts $\\psi_j:B_1\\to Y$\, with $B_1$ the unit ball in $\
 \C^n$\, each chart being analytically extendable\, as a mapping to $Y$\, t
 o a four times larger concentric ball $B_4$. Main result of this paper is 
 an upper and lower bounds for the minimal number $\\kappa({\\U})$ of chart
 s in doubling coverings of a manifold $Y$\, being a compact part of a non-
 singular level hypersurface $Y=\\{P=c\\}$\, where $P$ is a polynomial on $
 \\C^n$ with non-degenerated critical points. We show that $\\kappa({\\U})$
  is of order $\\log({1}/{\\rho})$\, where $\\rho$ is the distance from $Y$
  to the singular set of $P$. Our main motivation is that doubling covering
 s form a special class of "smooth parameterizations"\, which are used in b
 ounding entropy type invariants in smooth dynamics on one side\, and in bo
 unding density of rational points in diophantine geometry on the other. Co
 mplexity of smooth parameterizations is a key issue in some important open
  problems in both areas. We also present connections between doubling cove
 rings and doubling inequalities for analytic functions $f$ on $Y$\, which 
 compare the maxima of $|f|$ on couples of compact domains $\\Omega\\subset
  G$ in $Y$. We shortly indicate connections with Kobayashi metric and with
  Harnack inequality.\nhttps://arxiv.org/abs/1512.02903\n
CATEGORIES:Séminaire,Analyse et Géométrie
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