THE KOBAYASHI k-METRICS ON COMPLEX SPACES

Thai, Do Duc; Duc, Pham Viet

doi:10.1142/s0129167x99000392

Cited by 4 publications

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We notice that Thai [24] gave a shorter proof of this result. Now, we give a characterization of the hyperbolicity of complex spaces using these k-metrics.…”

Section: The Hyperbolicity Of Complex Spacesmentioning

confidence: 85%

The moduli space of hyperbolic compact complex spaces

Khalfallah

2006

Math. Z.

View full text Add to dashboard Cite

In this paper, we construct the moduli space of reduced hyperbolic compact complex spaces. First, we prove an infinitesimal characterization of hyperbolicity using a family of Kobayashi-Royden pseudo-metrics introduced by Venturini and as a consequence we conclude that the property of Landau holds for complex spaces. Finally, we establish this moduli space in the case of locally trivial deformations, and in a more general situation, the case of equisingular deformations. IntroductionBrody [1] and Wright [26] constructed the moduli space of compact hyperbolic manifolds. In [11], the author generalized this result by establishing the moduli space of hyperbolically imbedded manifolds, which can be seen as a non compact version of the moduli space of Brody-Wright. To construct this moduli space, we use a general criterion to represent analytic functors by coarse moduli spaces. This criterion is due to Suchmacher [21] and Fujiki [6]. See also Kosarew and Okonek [17] for further generalizations.We notice that Fujiki [6] and Schumacher [20] used this criterion to construct the moduli space of polarized kähler manifolds.The paper is divided in three parts. In the first part, we prove that the property of Landau holds also for complex spaces and not only for manifolds [9] or for complex spaces with isolated singularities [23]. This can be achieved by a characterization of the hyperbolicity expressed with the help of the family {K k X }, the Kobayashi infinitesimal k-pseudo-metrics introduced by Venturini [25]. Royden [19] proved a similar characterization in the case of complex manifolds. A. Khalfallah (B) Institut Préparatoire aux études d'ingénieur, Rue Ibn El Jazzar,

show abstract

“…We notice that Thai [24] gave a shorter proof of this result. Now, we give a characterization of the hyperbolicity of complex spaces using these k-metrics.…”

Section: The Hyperbolicity Of Complex Spacesmentioning

confidence: 85%

The moduli space of hyperbolic compact complex spaces

Khalfallah

2006

Math. Z.

View full text Add to dashboard Cite

show abstract

On Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces

Trang

Trao

2021

Acta Math Vietnam

View full text Add to dashboard Cite

On the hyperbolic imbeddedness modulo a closed subset of complex spaces

Trang,

Thai,

Trao

et al. 2024

Int. J. Math.

View full text Add to dashboard Cite

In this paper, we will focus on characterizing the hyperbolic imbeddedness modulo a closed subset of complex spaces, hoping that our results will be useful to people working on that subject. Firstly, we give criteria of the hyperbolic imbeddedness modulo a closed subset of (singular) complex spaces. Secondly, we study the hyperbolic imbeddedness modulo a closed subset of some classes of (singular) complex spaces.

show abstract

THE KOBAYASHI k-METRICS ON COMPLEX SPACES

Cited by 4 publications

References 5 publications

The moduli space of hyperbolic compact complex spaces

The moduli space of hyperbolic compact complex spaces

On Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces

On the hyperbolic imbeddedness modulo a closed subset of complex spaces

Contact Info

Product

Resources

About