SINGULAR LOCI IN HOLOMORPHIC FAMILIES

1998 ◽  
Vol 09 (03) ◽  
pp. 277-293
Author(s):  
ADAM HARRIS
Keyword(s):  
Vector Bundles ◽  
A Priori ◽  
Complex Structure ◽  
Compact Complex Manifold ◽  
Entire Family ◽  
Analytic Subset ◽  
Degeneracy Loci ◽  
Singular Spaces ◽  
Singular Loci ◽  
Complex Projective

Let [Formula: see text] be a proper flat morphism between manifolds, and [Formula: see text] an analytic subset, such that the fibres Xt, for all [Formula: see text], determine a locally trivial deformation of a compact complex manifold. Non-generic fibres Xt, for t ∈ A, may be taken a priori to be singular spaces, or to have a smooth complex structure which is biholomorphically distinct from their generic neighbours. The main theorem of this article provides a sufficient condition for local triviality of the entire family [Formula: see text], in terms of the dimension of A and of the singular subvarieties of certain "degeneracy loci" in [Formula: see text]. Several specific applications of the main theorem are subsequently examined, some of which correspond sharply with examples of "structure-jumping" in complex deformations and "jumping loci" of vector bundles on complex projective space.

Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1

1993 ◽  
Vol 114 (3) ◽  
pp. 443-451
Author(s):  
Al Vitter
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Vector Bundles ◽  
Einstein Metrics ◽  
Einstein Metric ◽  
Holomorphic Vector Bundles ◽  
Kähler Form ◽  
Points Of View ◽  
The Stability ◽  
Complex Projective

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).

Ample Vector Bundles of Curve Genus One

1999 ◽  
Vol 42 (2) ◽  
pp. 209-213 ◽  
Author(s):  
Antonio Lanteri ◽  
Hidetoshi Maeda
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Ample Vector Bundle ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Curve Genus ◽  
Genus One ◽  
Complex Projective ◽  
Zero Locus

AbstractWe investigate the pairs (X, ε) consisting of a smooth complex projective variety X of dimension n and an ample vector bundle ε of rank n − 1 on X such that ε has a section whose zero locus is a smooth elliptic curve.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

Remarks on Kähler–Ricci solitons

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Lucio Bedulli ◽  
Anna Gori
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Ricci Soliton ◽  
Compact Complex Manifold ◽  
Ricci Solitons ◽  
Complex Projective

AbstractWe prove that a compact complex manifold endowed with a Kähler-Ricci soliton cannot be isometrically embedded in a complex projective space ℂℙ

Pattern Recognition and Geochemical Data: An Application to Monteregian Hills

1974 ◽  
Vol 11 (11) ◽  
pp. 1577-1585 ◽  
Author(s):  
Michel Dagbert ◽  
Michel David
Keyword(s):  
Pattern Recognition ◽  
A Priori ◽  
Complex Structure ◽  
Geochemical Data ◽  
Factor Space ◽  
Rock Unit ◽  
Minor Elements ◽  
Large Sets ◽  
Comprehensive Picture ◽  
Representative Points

The development of rapid and efficient methods of chemical analysis of major and minor elements in rocks has given rise to the production of large sets of data constituting a comprehensive 'picture' of the chemical composition of a rock unit or a rock group in a given area.The complex structure of this multidimensional picture is globally analyzed by 'correspondence analysis' as an interpretative method of pattern recognition. Significative trends of variation are determined and expressed in geological terms. Density distribution of representative points in the factor space is evaluated in search of homogeneous substructures inside the global one. The resulting 'natural clustering' is compared to an a priori partitioning of the structure on the basis of petrographic criteria.The whole analysis is performed by a computer program that can accommodate some 600 samples measured on more than 20 variables. The analysis of a chemical picture of the Monteregian petrographic province is given to illustrate the method.

scholarly journals Model of forming a spatial-temporary radio frequency portrait of subscriber terminals in satellite communication systems monitoring

2020 ◽  
Vol 100 (4) ◽  
pp. 78-86
Author(s):  
M. Baldychev ◽  
◽  
A. Bosyy ◽  
O. Galtseva ◽  
Keyword(s):  
Radio Frequency ◽  
Software Defined Radio ◽  
Communication Systems ◽  
Satellite Communication ◽  
A Priori ◽  
Complex Structure ◽  
Satellite Communications ◽  
Physical Parameters ◽  
Time Frequency ◽  
Spatio Temporal

Currently, the development of satellite communications systems (SCS) is associated with the development of signals of complex structure. The popularization and distribution of software-defined radio systems (Software-defined radio, SDR) are noted, which leads to a decrease of quality of functioning of the SCS. Promising areas of countering the unauthorized use of the time-frequency resource of the KA repeater are methods aimed at determining the location of subscriber terminals (ST) and analyzing the service and semantic parts of the transmitted message. Accounting for changes of physical parameters requires the use of a large amount of heterogeneous a priori data; it is not achievable task in practice. According to the theory of mathematical statistics, the approximation is used at solving problems of sample analysis. The result of the approximation is a spatio-temporal radio-frequency portrait (STRFP) of an ST participating in the formation of a group signal. Thus, the aim of the research is to develop a model of changing the physical parameters of a radio signal and to study the possibility of approximating physical parameters in order to form a spatio-temporal radiofrequency portrait of an ST SCS.

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