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SUMMARY:Hyperbolicity of symmetric powers via Nevanlinna theory - Natalia 
 Garcia Fritz (Pontificia Universidad Católica de Chile)
DTSTART:20240321T140000Z
DTEND:20240321T150000Z
UID:TALK209467@talks.cam.ac.uk
DESCRIPTION:The Green--Griffiths--Lang conjecture is regarded as a central
  problem in arithmetic geometry\, as it relates the notion of complex hype
 rbolicity of a variety to its geometric properties and the distribution of
  its rational points. In particular\, the case of m-th symmetric powers of
  varieties is related to the distribution of algebraic points of degree at
  most m. By using the theory of jet differentials\, in 2022 Cadorel\, Camp
 ana\, and Rousseau gave geometric conditions to obtain pseudo-hyperbolicit
 y of symmetric powers of varieties\, which was applied\, for instance\, to
  obtain hyperbolicity for symmetric powers of generic hypersurfaces of hig
 h degree. In this talk\, we will show a new technique coming from Nevanlin
 na theory that gives geometric criteria to obtain hyperbolicity of symmetr
 ic powers of varieties. Using this method\, we provide concrete examples o
 f varieties with hyperbolic symmetric powers. This is joint work with Hect
 or Pasten.
LOCATION:Seminar Room 1\, Newton Institute
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