Complex Algebraic Foliations

Author : Alcides Lins Neto,Bruno Scárdua
Publisher : Walter de Gruyter GmbH & Co KG
Page : 249 pages
File Size : 44,6 Mb
Release : 2020-02-24
Category : Mathematics
ISBN : 9783110602050

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Complex Algebraic Foliations by Alcides Lins Neto,Bruno Scárdua Pdf

This book is a basic reference in the modern theory of holomorphic foliations, presenting the interplay between various aspects of the theory and utilizing methods from algebraic and complex geometry along with techniques from complex dynamics and several complex variables. The result is a solid introduction to the theory of foliations, covering basic concepts through modern results on the structure of foliations on complex projective spaces.

Author : Paolo Cascini,James McKernan,Jorge Vitório Pereira
Publisher : Springer
Page : 216 pages
File Size : 47,7 Mb
Release : 2016-03-30
Category : Mathematics
ISBN : 9783319244600

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Foliation Theory in Algebraic Geometry by Paolo Cascini,James McKernan,Jorge Vitório Pereira Pdf

Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions. Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study./div

Author : Alcides Lins Neto,Bruno Scárdua
Publisher : de Gruyter
Page : 0 pages
File Size : 55,7 Mb
Release : 2020
Category : Mathematics
ISBN : 3110601079

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Complex Algebraic Foliations by Alcides Lins Neto,Bruno Scárdua Pdf

This book is a basic reference in the modern theory of holomorphic foliations, presenting the interplay between various aspects of the theory and utilizing methods from algebraic and complex geometry along with techniques from complex dynamics and s

Author : Marco Brunella
Publisher : Springer
Page : 140 pages
File Size : 46,9 Mb
Release : 2015-03-25
Category : Mathematics
ISBN : 9783319143101

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Birational Geometry of Foliations by Marco Brunella Pdf

The text presents the birational classification of holomorphic foliations of surfaces. It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces in the spirit of the classification of complex algebraic surfaces.

Author : Bruno Scardua,Carlos Arnoldo Morales Rojas
Publisher : World Scientific
Page : 196 pages
File Size : 42,7 Mb
Release : 2017-02-16
Category : Mathematics
ISBN : 9789813207097

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Geometry, Dynamics And Topology Of Foliations: A First Course by Bruno Scardua,Carlos Arnoldo Morales Rojas Pdf

The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments.In a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.

Author : Xiaolu Wang
Publisher : Springer
Page : 171 pages
File Size : 55,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540479154

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On the C*-Algebras of Foliations in the Plane by Xiaolu Wang Pdf

The main result of this original research monograph is the classification of C*-algebras of ordinary foliations of the plane in terms of a class of -trees. It reveals a close connection between some most recent developments in modern analysis and low-dimensional topology. It introduces noncommutative CW-complexes (as the global fibred products of C*-algebras), among other things, which adds a new aspect to the fast-growing field of noncommutative topology and geometry. The reader is only required to know basic functional analysis. However, some knowledge of topology and dynamical systems will be helpful. The book addresses graduate students and experts in the area of analysis, dynamical systems and topology.

Author : Felipe Cano
Publisher : Springer Nature
Page : 500 pages
File Size : 53,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031541728

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Handbook of Geometry and Topology of Singularities VI: Foliations by Felipe Cano Pdf

Author : Felipe Cano
Publisher : Springer Nature
Page : 531 pages
File Size : 54,6 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031524813

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Handbook of Geometry and Topology of Singularities V: Foliations by Felipe Cano Pdf

Author : Sławomir Dinew,Sebastien Picard,Andrei Teleman,Alberto Verjovsky
Publisher : Springer Nature
Page : 242 pages
File Size : 40,6 Mb
Release : 2019-11-05
Category : Mathematics
ISBN : 9783030258832

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Complex Non-Kähler Geometry by Sławomir Dinew,Sebastien Picard,Andrei Teleman,Alberto Verjovsky Pdf

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sławomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.

Author : Bruno Scárdua
Publisher : Springer Nature
Page : 172 pages
File Size : 53,9 Mb
Release : 2021-12-01
Category : Mathematics
ISBN : 9783030767051

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Holomorphic Foliations with Singularities by Bruno Scárdua Pdf

This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H. Cartan, K. Oka, T. Nishino, and M. Suzuki. The text starts with a gentle presentation of the classical notion of foliations, advancing to holomorphic foliations and then holomorphic foliations with singularities. The theory behind reduction of singularities is described in detail, as well the cases for dynamics of a local diffeomorphism and foliations on complex projective spaces. A final chapter brings recent questions in the field, as holomorphic flows on Stein spaces and transversely homogeneous holomorphic foliations, along with a list of open questions for further study and research. Selected exercises at the end of each chapter help the reader to grasp the theory. Graduate students in Mathematics with a special interest in the theory of foliations will especially benefit from this book, which can be used as supplementary reading in Singularity Theory courses, and as a resource for independent study on this vibrant field of research.

Author : Terence Gaffney,Maria Aparecida Soares Ruas
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 54,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836651

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Real and Complex Singularities by Terence Gaffney,Maria Aparecida Soares Ruas Pdf

The Workshop on Real and Complex Singularities is held every other year at the Instituto de Ciencias Matematicas e de Computacao (Sao Carlos, Brazil) and brings together specialists in the vanguard of singularities and its applications. This volume contains articles contributed by participants of the seventh workshop.

Author : Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi
Publisher : Springer
Page : 553 pages
File Size : 55,9 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9783319736396

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Singularities and Foliations. Geometry, Topology and Applications by Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi Pdf

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

Author : I͡U. S. Ilʹi͡ashenko,Julij S. Ilʹjašenko,Yulij Ilyashenko,Û. S. Ilʹâšenko (mathématicien).),I︠U︡. S. Ilʹi︠a︡shenko,S. Yakovenko
Publisher : American Mathematical Soc.
Page : 641 pages
File Size : 40,7 Mb
Release : 2008
Category : Analytic spaces
ISBN : 9780821836675

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Lectures on Analytic Differential Equations by I͡U. S. Ilʹi͡ashenko,Julij S. Ilʹjašenko,Yulij Ilyashenko,Û. S. Ilʹâšenko (mathématicien).),I︠U︡. S. Ilʹi︠a︡shenko,S. Yakovenko Pdf

The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.

Author : Donald G. Babbitt,Jane E. Kister
Publisher : American Mathematical Soc.
Page : 762 pages
File Size : 55,7 Mb
Release : 2000-05-05
Category : Mathematics
ISBN : 0821896709

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Featured Reviews in Mathematical Reviews 1997-1999 by Donald G. Babbitt,Jane E. Kister Pdf

This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Author : Danny Calegari
Publisher : Oxford University Press on Demand
Page : 378 pages
File Size : 51,9 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780198570080

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Foliations and the Geometry of 3-Manifolds by Danny Calegari Pdf

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.