On Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces

2021 ◽  
Author(s):  
Pham Nguyen Thu Trang ◽  
Nguyen Van Trao
Keyword(s):  
Closed Subset ◽  
Complex Spaces ◽  
Singular Complex Spaces

BOCHNER–MARTINELLI FORMULAS ON SINGULAR COMPLEX SPACES

2010 ◽  
Vol 21 (02) ◽  
pp. 225-253 ◽  
Author(s):  
VINCENZO ANCONA ◽  
BERNARD GAVEAU
Keyword(s):  
Projective Variety ◽  
Complex Space ◽  
Closed Subspace ◽  
Hodge Structure ◽  
Integral Formula ◽  
Mixed Hodge Structure ◽  
Complex Spaces ◽  
Residue Formula ◽  
Complex Dimension ◽  
Singular Complex Spaces

Let U be a complex space of complex dimension n ≥ 2, P a point of U, π : Ũ → U a modification such that Ũ is nonsingular and D = π-1 (P) is a divisor with normal crossings. A Bochner–Martinelli form on U\{P} is a [Formula: see text]-closed differential form ω on Ũ\D, of pure type (n,n - 1), logarithmic along D. Such form detects a cohomology class of H2n - 1 (U\{P},ℂ) on the singular space U\{P}. Thanks to a general residue formula we prove that the forms ω give rise to an integral formula of Bochner–Martinelli type for holomorphic functions. If U satisfies the following assumption that {there exists a compact complex space X bimeromorphic to a Kähler manifold, and a closed subspace T ⊂ X, such that X\T = U (an affine, or a quasi-projective variety satisfies the above property), we relate Bochner–Martinelli forms to the mixed Hodge structure carried by H2n-1 (U\{P},ℂ). Most of our results hold for complex spaces which are not Stein.

scholarly journals The Poletsky-Rosay theorem on singular complex spaces

2012 ◽  
Vol 61 (4) ◽  
pp. 1407-1423 ◽  
Author(s):  
Barbara Drinovec Drnovsek ◽  
Franc Forstneric
Keyword(s):  
Complex Spaces ◽  
Singular Complex Spaces

scholarly journals UNDERGROUND SURVEYING: 16<sup>TH</sup> CENTURY CELLAR VAULTS IN THE GALERÍA DE CONVALECIENTES, MONASTERY OF SAN LORENZO DEL ESCORIAL

2017 ◽  
Vol XLII-2/W3 ◽  
pp. 179-186 ◽  
Author(s):  
P. Chías ◽  
T. Abad ◽  
E. Echeverría ◽  
M. De Miguel ◽  
P. Llorente
Keyword(s):  
3D Model ◽  
Geodetic Network ◽  
Control Points ◽  
Architectural Heritage ◽  
San Lorenzo ◽  
Complex Spaces ◽  
Singular Complex Spaces ◽  
Essential Problem

Underground surveying of cellars, caves, and architectural spaces, is quite different from surveying on the surface. Researchers must deal with various challenges derived of the lack of natural light, low temperature, and humidity, but also with inaccessibility. But the essential problem in underground surveying is that of orientating the underground surveys to the surface surveys. For this purpose our methodology integrates different geomatic techniques, as the use of a scanner laser in order to obtain a 3D model, as well as classic topography, and GPS to locate accurately the control points according to the official reference frame of the Spanish Geodetic Network. The developed methodology is described and applied to the case study of the cellars of the Gallery of Convalescents (Galería de Convalecientes) in the Royal Monastery of San Lorenzo de El Escorial. These cellars compose an outstanding series of interrelated singular complex spaces. Their study is particularly relevant because of the quality of the stonework, the geometry of the vaults and lunettes, and the stereotomy. The fact that these spaces were neither surveyed nor studied before, must be stressed. And our work will bring into light an important part of the 16th century Spanish architectural heritage. Finally, the INSPIRE Directive becomes an opportunity to integrate cultural heritage datasets into an interoperable framework, and to share and diffuse them as geographic information.

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

Shelah's work on non-semi-proper iterations, II

2001 ◽  
Vol 66 (4) ◽  
pp. 1865-1883 ◽  
Author(s):  
Chaz Schlindwein
Keyword(s):  
Closed Subset ◽  
Stationary Subset ◽  
Finite Support ◽  
Countable Support ◽  
Final Model ◽  
Axiom A ◽  
Mahlo Cardinal ◽  
The One ◽  
Image Position ◽  
Special Case

One of the main goals in the theory of forcing iteration is to formulate preservation theorems for not collapsing ω1 which are as general as possible. This line leads from c.c.c. forcings using finite support iterations to Axiom A forcings and proper forcings using countable support iterations to semi-proper forcings using revised countable support iterations, and more recently, in work of Shelah, to yet more general classes of posets. In this paper we concentrate on a special case of the very general iteration theorem of Shelah from [5, chapter XV]. The class of posets handled by this theorem includes all semi-proper posets and also includes, among others, Namba forcing.In [5, chapter XV] Shelah shows that, roughly, revised countable support forcing iterations in which the constituent posets are either semi-proper or Namba forcing or P[W] (the forcing for collapsing a stationary co-stationary subset ofwith countable conditions) do not collapse ℵ1. The iteration must contain sufficiently many cardinal collapses, for example, Levy collapses. The most easily quotable combinatorial application is the consistency (relative to a Mahlo cardinal) of ZFC + CH fails + whenever A ∪ B = ω2 then one of A or B contains an uncountable sequentially closed subset. The iteration Shelah uses to construct this model is built using P[W] to “attack” potential counterexamples, Levy collapses to ensure that the cardinals collapsed by the various P[W]'s are sufficiently well separated, and Cohen forcings to ensure the failure of CH in the final model.In this paper we give details of the iteration theorem, but we do not address the combinatorial applications such as the one quoted above.These theorems from [5, chapter XV] are closely related to earlier work of Shelah [5, chapter XI], which dealt with iterated Namba and P[W] without allowing arbitrary semi-proper forcings to be included in the iteration. By allowing the inclusion of semi-proper forcings, [5, chapter XV] generalizes the conjunction of [5, Theorem XI.3.6] with [5, Conclusion XI.6.7].

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

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