Limits of Calabi–Yau metrics when the Kähler class degenerates
Valentino Tosatti (2009)
Journal of the European Mathematical Society
Shuzo Izumi (1981/1982)
Inventiones mathematicae
Andrey Todorov (2003)
Revista Matemática Iberoamericana
In this paper we review the moduli theory of polarized CY manifolds. We briefly sketched Kodaira-Spencer-Kuranishi local deformation theory developed by the author and G. Tian. We also construct the Teichmüller space of polarized CY manifolds following the ideas of I. R. Shafarevich and I. I. Piatetski-Shapiro. We review the fundamental result of E. Viehweg about the existence of the course moduli space of polarized CY manifolds as a quasi-projective variety. Recently S. Donaldson computed the moment...
W.M. Goldman, J.J. Millson (1987)
Inventiones mathematicae
Nikolai Nikolov, Peter Pflug (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Some known localization results for hyperconvexity, tautness or -completeness of bounded domains in are extended to unbounded open sets in .
H. Esnault, E. Viehweg (1986)
Inventiones mathematicae
Gerd Dethloff, Steven S.-Y. Lu (2007)
Annales de l’institut Fourier
In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity and logarithmic Kodaira dimension , any...
Joël Merker (2009)
Annales de l’institut Fourier
For low order jets, it is known how to construct meromorphic frames on the space of the so-called vertical -jets of the universal hypersurfaceparametrizing all projective hypersurfaces of degree . In 2004, for , Siu announced that there exist two constants and such that the twisted tangent bundleis generated at every point by its global sections. In the present article, we establish this property outside a certain exceptional algebraic subset defined by the vanishing of certain Wronskians,...
Jérôme Tambour (2012)
Annales de l’institut Fourier
LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization....
Zbigniew Jelonek (2009)
Colloquium Mathematicae
We show that if X, Y are smooth, compact k-dimensional submanifolds of ℝⁿ and 2k+2 ≤ n, then each diffeomorphism ϕ: X → Y can be extended to a diffeomorphism Φ: ℝⁿ → ℝⁿ which is tame (to be defined in this paper). Moreover, if X, Y are real analytic manifolds and the mapping ϕ is analytic, then we can choose Φ to be also analytic. We extend this result to some interesting categories of closed (not necessarily compact) subsets of ℝⁿ, namely, to the category of Nash submanifolds...
Le Mau Hai, Nguyen Van Khue (1992)
Annales de l'institut Fourier
The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.
François Berteloot (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
Nous mettons en perspective différentes méthodes de changement d’échelles et illustrons leur pertinence en mettant sur pieds des preuves simples et élémentaires de plusieurs théorèmes biens connus en analyse ou géométrie complexe. Les situations abordées sont variées et la plupart des théorèmes démontrés sont des classiques initialement obtenus entre la fin du xixe et la seconde moitié du xxe siècle.
Frédéric Campana, Henri Guenancia, Mihai Păun (2013)
Annales scientifiques de l'École Normale Supérieure
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.
Jean-Pierre Bourguignon (1996/1997)
Séminaire Bourbaki
Olivier Biquard (2004/2005)
Séminaire Bourbaki
Un des problèmes les plus intéressants de la géométrie différentielle complexe consiste à comprendre les classes de Kähler de variétés complexes admettant des métriques à courbure scalaire constante. La question de l’unicité a été récemment résolue par Donaldson, Mabuchi, Chen–Tian. Des liens forts avec la stabilité algébrique des variétés ont été mis en évidence. L’exposé s’attachera à exposer les idées nouvelles qui ont mené à ces résultats.
E. Calabi (1979)
Annales scientifiques de l'École Normale Supérieure
Zapiski naucnych seminarov POMI
Hong-Jong Kim (1987)
Mathematische Zeitschrift
Junjiro Noguchi (1988)
Inventiones mathematicae
M. Lübke, C. Okonek (1986)
Mathematische Annalen