scholarly journals Biholomorphisms between Hartogs domains over homogeneous Siegel domains

2018 ◽  
Vol 29 (08) ◽  
pp. 1850057
Author(s):  
Aeryeong Seo
Keyword(s):  
Automorphism Groups ◽  
Type Ii ◽  
Holomorphic Map ◽  
Siegel Domains ◽  
Proper Holomorphic Map ◽  
Hartogs Domains

In this paper, we characterize the Hartogs domains over homogeneous Siegel domains of type II and explicitly describe their automorphism groups. Moreover, we prove that any proper holomorphic map between equidimensional Hartogs domains over homogeneous Siegel domains of type II is a biholomorphism.

scholarly journals Type II degenerations of K3 surfaces

1985 ◽  
Vol 99 ◽  
pp. 11-30 ◽  
Author(s):  
Shigeyuki Kondo
Keyword(s):  
Number Field ◽  
Complex Manifold ◽  
Complex Number ◽  
Three Dimensional ◽  
K3 Surfaces ◽  
Type Ii ◽  
Holomorphic Map ◽  
Canonical Class ◽  
Proper Holomorphic Map ◽  
Complex Number Field

A degeneration of K3 surfaces (over the complex number field) is a proper holomorphic map π: X→Δ from a three dimensional complex manifold to a disc, such that, for t ≠ 0, the fibres Xt = π-1(t) are smooth K3 surfaces (i.e. surfaces Xt with trivial canonical class KXt = 0 and dim H1(Xt, Oxt) = 0).

KORÁNYI’S LEMMA FOR HOMOGENEOUS SIEGEL DOMAINS OF TYPE II. APPLICATIONS AND EXTENDED RESULTS

2014 ◽  
Vol 90 (1) ◽  
pp. 77-89 ◽  
Author(s):  
DAVID BÉKOLLÉ ◽  
HIDEYUKI ISHI ◽  
CYRILLE NANA
Keyword(s):  
Functional Analysis ◽  
Bergman Kernel ◽  
Atomic Decomposition ◽  
Bergman Spaces ◽  
Decomposition Theorem ◽  
Interpolation Theorem ◽  
Type Ii ◽  
Siegel Domain ◽  
Homogeneous Case ◽  
Siegel Domains

AbstractWe show that the modulus of the Bergman kernel $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}B(z, \zeta )$ of a general homogeneous Siegel domain of type II is ‘almost constant’ uniformly with respect to $z$ when $\zeta $ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used it to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces $A^p$ on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents $p$ via functional analysis using recent estimates.

scholarly journals Hua System and Pluriharmonicity for Symmetric Irreducible Siegel Domains of Type II

2002 ◽  
Vol 188 (1) ◽  
pp. 38-74 ◽  
Author(s):  
Aline Bonami ◽  
Dariusz Buraczewski ◽  
Ewa Damek ◽  
Andrzej Hulanicki ◽  
Richard Penney ◽  
...  
Keyword(s):  
Type Ii ◽  
Siegel Domains

On Möbius Spaces Admitting Automorphism Groups of Type II.2

2011 ◽  
Vol 59 (3-4) ◽  
pp. 301-318
Author(s):  
Hans-Joachim Kroll ◽  
Sayed-Ghahreman Taherian
Keyword(s):  
Automorphism Groups ◽  
Type Ii

Bergman–Hartogs domains and their automorphisms

2019 ◽  
pp. 316-323
Author(s):  
Guy ROOS
Keyword(s):  
Automorphism Groups ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
Homogeneous Domain ◽  
Hartogs Domains ◽  
Bounded Homogeneous Domain

For Cartan–Hartogs domains and also for Bergman–Hartogs domains, the determination of their automorphism groups is given for the cases when the base is any bounded symmetric domain and a general bounded homogeneous domain respectively.

scholarly journals Holomorphic isometries between products of complex unit balls

2017 ◽  
Vol 28 (09) ◽  
pp. 1740010 ◽  
Author(s):  
Shan Tai Chan ◽  
Ming Xiao ◽  
Yuan Yuan
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Closed Unit Disk ◽  
Holomorphic Map ◽  
Proper Holomorphic Map ◽  
Poincaré Disk

We first give an exposition on holomorphic isometries from the Poincaré disk to polydisks and from the Poincaré disk to the product of the Poincaré disk with a complex unit ball. As an application, we provide an example of proper holomorphic map from the unit disk to the complex unit ball that is irrational, algebraic and holomorphic on a neighborhood of the closed unit disk. We also include some new results on holomorphic isometries.

Sign in / Sign up

Export Citation Format

Share Document