scholarly journals Weighted Koppelman formulas and the ∂¯-equation on an analytic space

2011 ◽  
Vol 261 (3) ◽  
pp. 777-802 ◽  
Author(s):  
Mats Andersson ◽  
Håkan Samuelsson
Keyword(s):  
Analytic Space ◽  
Koppelman Formulas

scholarly journals Koppelman formulas on Grassmannians

2010 ◽  
Vol 2010 (640) ◽  
Author(s):  
Elin Götmark ◽  
Håkan Samuelsson ◽  
Henrik Seppänen
Keyword(s):  
Koppelman Formulas

scholarly journals Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle

2019 ◽  
Vol 2019 (749) ◽  
pp. 87-132
Author(s):  
Laurent Meersseman
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Classical Case ◽  
Analytic Space ◽  
Fundamental Result ◽  
Compact Complex Manifold ◽  
Complex Structures ◽  
Analogous Statement ◽  
Finite Dimensional ◽  
Cr Structures

Abstract Kuranishi’s fundamental result (1962) associates to any compact complex manifold {X_{0}} a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to {X_{0}} . In this paper, we give an analogous statement for Levi-flat CR-manifolds fibering properly over the circle by associating to any such {\mathcal{X}_{0}} the loop space of a finite-dimensional analytic space which serves as a local moduli space of CR-structures close to {\mathcal{X}_{0}} . We then develop in this context a Kodaira–Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.

scholarly journals Wonderful compactifications of Bruhat-Tits buildings

2017 ◽  
Vol Volume 1 ◽  
Author(s):  
Bertrand Remy ◽  
Amaury Thuillier ◽  
Annette Werner
Keyword(s):  
Local Field ◽  
Semisimple Group ◽  
The Other ◽  
Analytic Space ◽  
Ground Field ◽  
Berkovich Analytic Space ◽  
Euclidean Building ◽  
The Relationship

Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by embedding the building in the Berkovich analytic space associated to the wonderful compactification of the group. The construction of this embedding map is achieved over a general non-archimedean complete ground field. The relationship between the structures at infinity, one coming from strata of the wonderful compactification and the other from Bruhat-Tits buildings, is also investigated.

scholarly journals Holomorphic automorphisms and cancellation theorems

1981 ◽  
Vol 81 ◽  
pp. 91-103 ◽  
Author(s):  
Toshio Urata
Keyword(s):  
Analytic Space ◽  
Biholomorphic Mapping ◽  
Direct Factor ◽  
Positive Dimension ◽  
Analytic Subvariety ◽  
Holomorphic Automorphisms ◽  
Complex Analytic Space

Let X be a complex analytic space of positive dimension and A a complex analytic subvariety of X. We call A a direct factor of X if there exist a complex analytic space B and a biholomorphic mapping f: A × B → X such that, for some b ∊ B, f(a, b) = a on A, and a complex analytic space X to be primary if X has no direct factor, not equal to X itself, of positive dimension.

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