Kähler-Einstein structures of general natural lifted type on the cotangent bundles.
Limits of Calabi–Yau metrics when the Kähler class degenerates
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.
Métriques d'Einstein-Kähler sur les variétés de Fano : obstructions et existence
Nadel's Subschemes of Fano Manifolds X with a Picard Group Pic(X) Isomorphic to Z
∗The author supported by Contract NSFR MM 402/1994.In this paper we find a global sufficient condition for suitable subschemes of Fano manifolds to be Nadel’s subschemes. We apply this condition to one-dimensional subschemes of a projective space.
On the Burns-Epstein invariants of spherical CR 3-manifolds
In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.
On the stability of the tangent bundle of Fano manifolds.
Orbifold Riemann surfaces and the Yang-Mills-Higgs equations
Seiberg Witten invariants and uniformizations.
Stability of the tangent bundle and existence of a Kähler-Einstein metric.
Stable triples, equivariant bundles and dimensional reduction.
Sur les inégalités de Morse holomorphes lorsque la courbure du fibré en droites est dégénérée
The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle
The purpose of this paper is to calculate the asymptotics of the Ray-Singer analytic torsion associated with the -th symmetric power of a holomorphic Hermitian positive vector bundle when tends to . We thus extend our previous results on positive line bundles.
The Bellaterra connection.
A new object is introduced - the "Fischer bundle". It is, formally speaking, an Hermitean bundle of infinite rank over a bounded symmetric domain whose fibers are Hilbert spaces whose elements can be realized as entire analytic functions square integrable with respect to a Gaussian measure ("Fischer spaces"). The definition was inspired by our previous work on the "Fock bundle". An even more general framework is indicated, which allows one to look upon the two concepts from a unified point of view....
The Kähler Ricci flow on Fano manifolds (I)
We study the evolution of pluri-anticanonical line bundles along the Kähler Ricci flow on a Fano manifold . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of . For example, the Kähler Ricci flow on converges when is a Fano surface satisfying or . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....
The Thullen type extension theorem for holomorphic vector bundles with L2-bounds on curvature.
Un théoreme de prolongement L2 de sections holomorphes d'un fibré hermitien.
Uniqueness of Kähler-Einstein cone metrics.
The purpose of this paper is to describe a method to construct a Kähler metric with cone singularity along a divisor and to illustrate a type of maximum principle for these incomplete metrics by showing that Kähler-Einstein metrics are unique in geometric Hölder spaces.
Yang-Mills connections over compact strongly pseudoconvex CR manifolds.