Remarques sur le revêtement universel des variétés kählériennes compactes
Connexité abélienne des variétés kählériennes compactes
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from . We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.
Projective manifolds whose tangent bundles are numerically effective.
Geometric stability of the cotangent bundle and the universal cover of a projective manifold
We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold have a pseudo-effective (instead of generically nef) determinant. A first consequence is that is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of is not covered by compact positive-dimensional analytic subsets,...
On the second exterior power of tangent bundles of threefolds
Appendix to the article of T. Peternell: the Kodaira dimension of Kummer threefolds
We prove that Kummer threefolds with algebraic dimension have Kodaira dimension 0.
Birational positivity in dimension
In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an provided that has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.
Représentations linéaires des groupes kählériens et de leurs analogues projectifs
Dans cette note nous établissons le résultat suivant, annoncé dans [
Numerical character of the effectivity of adjoint line bundles
In this note we show that, for any log-canonical pair , is -effective if its Chern class contains an effective -divisor. Then, we derive some direct corollaries.
Page 1