Inviluppi di olomorfia e gruppi di coomologia di Hausdorff
Isometries of Intrinsic Metrics on Strictly Convex Domains.
-holomorphic discs and real analytic hypersurfaces
We give in a real analytic almost complex structure , a real analytic hypersurface and a vector in the Levi null set at of , such that there is no germ of -holomorphic disc included in with and , although the Levi form of has constant rank. Then for any hypersurface and any complex structure , we give sufficient conditions under which there exists such a germ of disc.
Kähler manifolds with numerically effective Ricci class
Kähler manifolds with split tangent bundle
This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.
Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces
We determine all anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. Many of these admit a Kähler-Einstein metric and most of them do not have tigers.
Kähler-Einstein metrics singular along a smooth divisor
In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge...
Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor
Let be a compact Kähler manifold and be a -divisor with simple normal crossing support and coefficients between and . Assuming that is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on having mixed Poincaré and cone singularities according to the coefficients of . As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair .
Kähler-Einstein structures of general natural lifted type on the cotangent bundles.
-estimates for solutions of -equation on strongly -convex domains
La distance intégrée de Kobayashi sur une variété Banachique complexe
Nel caso di una varietà di Banach complessa , si costruisce una regolarizzata della metrica infinitesimale di Kobayashi. Se ne deduce una distanza integrata di Kobayashi e, se è iperbolica, si mostra che questa distanza è uguale alla distanza di Kobayashi.
La l-forme de torsion d'une variété hermitienne compacte.
La trace du noyau de la chaleur des variétés hyperboliques de dimension 3
Le problème du complémentaire d'une hypersurface holomorphe en analyse hyperbolique.
Lefschetz fibrations, complex structures and Seifert fibrations on .
Lelong numbers on projective varieties
Given a positive closed (1,1)-current defined on the regular locus of a projective variety with bounded mass near the singular part of and an irreducible algebraic subset of , we present uniform estimates for the locus inside where the Lelong numbers of are larger than the generic Lelong number of along .
Les fibrés de Seifert dans le problème de la simplification par les courbes elliptiques.
Levi equation for almost complex structures.
Levi-flat filling of real two-spheres in symplectic manifolds (I)
Let be a manifold with an almost complex structure tamed by a symplectic form . We suppose that has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of can be foliated by the boundaries of pseudoholomorphic discs.
Levi-flat filling of real two-spheres in symplectic manifolds (II)
We consider a compact almost complex manifold with smooth Levi convex boundary and a symplectic tame form . Suppose that is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into . We prove a result on filling by holomorphic discs.