On the Moser Normal Form ata Non-Umbilic Point.
On the rigidity of horizontal slices.
On the stability of the tangent bundle of Fano manifolds.
On the Sum of the Hermitian Scalar Curvatures of a Compact Hermitian Manifold.
On the Topology of Complex Projective Manifolds.
On the universal coverings of algebraic surfaces
On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold
This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle is nef, then for any ε >...
On the -equation in a Banach space
On weighted Bergman kernels of bounded domains
We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains for admissible weights .
Orbifold Riemann surfaces and the Yang-Mills-Higgs equations
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 Inv. Math. 63 (1981). 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.
Partial integrability on Thurston manifolds
We determine the maximal number of independent holomorphic functions on the Thurston manifolds , r ≥ 1, which are the first discovered compact non-Kähler almost Kähler manifolds. We follow the method which involves analyzing the torsion tensor dθ modθ, where are independent (1,0)-forms.
Periodische Abbildungen unitärer Mannigfaltigkeiten.
Plane curves with hyperbolic and -hyperbolic complements
Pluri-canonical divisors on Kähler manifolds.
Pluriclosed flow on manifolds with globally generated bundles
We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.
Pointed -surfaces
Let be a Riemann surface. Let be the -dimensional hyperbolic space and let be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping . If is a convex immersion, and if is its exterior normal vector field, we define the Gauss lifting, , of by . Let be the Gauss-Minkowski mapping. A solution to the Plateau problem is a convex immersion of constant Gaussian curvature equal to such that the Gauss lifting is complete and . In this paper, we show...
Polydiscs in Complex Manifolds.
Polynomial structures on principal fibre bundles