scholarly journals Classification of holomorphic foliations on Hopf manifolds

2015 ◽  
Vol 365 (1-2) ◽  
pp. 579-593 ◽  
Author(s):  
Maurício Corrêa ◽  
Arturo Fernández-Pérez ◽  
Antonio M. Ferreira
Keyword(s):  
Holomorphic Foliations ◽  
Hopf Manifolds

scholarly journals Finitely curved orbits of complex polynomial vector fields

2007 ◽  
Vol 79 (1) ◽  
pp. 13-16
Author(s):  
Albetã C. Mafra
Keyword(s):  
Vector Field ◽  
Gaussian Curvature ◽  
Algebraic Curve ◽  
Vector Fields ◽  
Complex Polynomial ◽  
Holomorphic Foliations ◽  
Holomorphic Curve ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?

scholarly journals Classification of regular dicritical foliations

2016 ◽  
Vol 37 (5) ◽  
pp. 1443-1479 ◽  
Author(s):  
GABRIEL CALSAMIGLIA ◽  
YOHANN GENZMER
Keyword(s):  
Vector Space ◽  
Normal Forms ◽  
Blow Up ◽  
The Other ◽  
Holomorphic Foliations ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Finite Dimensional ◽  
Birational Transformation

In this paper we give complete analytic invariants for the set of germs of holomorphic foliations in $(\mathbb{C}^{2},0)$ that become regular after a single blow-up. Some of the invariants describe the holonomy pseudogroup of the germ and are called transverse invariants. The other invariants lie in a finite dimensional complex vector space. Such singularities admit separatrices tangentially to any direction at the origin. When enough separatrices are leaves of a radial foliaton (a condition that can always be attained if the multiplicity of the germ at the origin is at most four) we are able to describe and realize all the analytical invariants geometrically and provide analytic normal forms. As a consequence, we prove that any two such germs sharing the same transverse invariants are conjugated by a very particular type of birational transformation. We also provide explicit examples of universal equisingular unfoldings of foliations that cannot be produced by unfolding functions. With these at hand we are able to explicitly parametrize families of analytically distinct foliations that share the same transverse invariants.

scholarly journals Classification of holomorphic Pfaff systems on Hopf manifolds

2021 ◽  
Author(s):  
Maurício Corrêa ◽  
Antonio M. Ferreira ◽  
Misha Verbitsky
Keyword(s):  
Hopf Manifolds

scholarly journals Topological Moduli Space for Germs of Holomorphic Foliations

2018 ◽  
Vol 2020 (23) ◽  
pp. 9228-9292
Author(s):  
David Marín ◽  
Jean-François Mattei ◽  
Éliane Salem
Keyword(s):  
Moduli Space ◽  
Topological Structure ◽  
Finite Dimension ◽  
Functional Space ◽  
Topological Classification ◽  
Topological Invariants ◽  
Holomorphic Foliations ◽  
Infinite Dimensional ◽  
Singular Foliations

Abstract This work deals with the topological classification of germs of singular foliations on $(\mathbb{C}^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho–Sad indices, and the projective holonomy representations and we compute the moduli space of topological classes in terms of the cohomology of a new algebraic object that we call group-graph. This moduli space may be an infinite-dimensional functional space but under generic conditions we prove that it has finite dimension and we describe its algebraic and topological structure.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

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