96 research outputs found
Weak analytic hyperbolicity of complements of generic surfaces of high degree in projective 3-space
In this article we prove that every entire curve in the complement of a
generic hypersurface of degree in is
algebraically degenerate i.e there exists a proper subvariety which contains
the entire curve.Comment: 11 page
Curves in Hilbert modular varieties
We prove a boundedness-theorem for families of abelian varieties with real
multiplication. More generally, we study curves in Hilbert modular varieties
from the point of view of the Green Griffiths-Lang conjecture claiming that
entire curves in complex projective varieties of general type should be
contained in a proper subvariety. Using holomorphic foliations theory, we
establish a Second Main Theorem following Nevanlinna theory. Finally, with a
metric approach, we establish the strong Green-Griffiths-Lang conjecture for
Hilbert modular varieties up to finitely many possible exceptions.Comment: Final version, to appear in Asian J. Mat
A survey on hyperbolicity of projective hypersurfaces
These are lecture notes of a course held at IMPA, Rio de Janiero, in
september 2010: the purpose was to present recent results on Kobayashi
hyperbolicity in complex geometry. Our ultimate goal is to describe the results
obtained on questions related to the geometry of entire curves traced in
generic complex projective hypersurfaces of high degree. For the convenience of
the reader, this survey tries to be as self contained as possible.Comment: 108 pages, 2 figure
Canonical surfaces with big cotangent bundle
Surfaces of general type with positive second Segre number are known to have
big cotangent bundle. We give a new criterion ensuring that a surface of
general type with canonical singularities has a minimal resolution with big
cotangent bundle. This provides many examples of surfaces with negative second
Segre number and big cotangent bundle.Comment: 11 pages. Comments welcom
KAWA lecture notes on complex hyperbolic geometry
International audienceThese lecture notes are based on a mini-course given at the fifth KAWA Winter School on March 24-29, 2014 at CIRM, Marseille. They provide an introduction to hyperbolicity of complex algebraic varieties namely the geometry of entire curves, and a description of some recent developments
Etude des jets de Demailly-Semple en dimension 3
Demailly-Semple jets are studied using the invariant theory of non reductive
groups. The geometric characterization of the 3-jets bundle in dimension 3 is
given and provides a Riemann-Roch computation.Comment: 25 pages, in french, final versio
- …