Complex Analytic Cycles I

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Complex Analytic Cycles I

Author : Daniel Barlet
Publisher : Springer Nature
ISBN 13 : 3030311635
Total Pages : 545 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Complex Analytic Cycles I by : Daniel Barlet

Download or read book Complex Analytic Cycles I written by Daniel Barlet and published by Springer Nature. This book was released on 2020-01-03 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of a presentation from scratch of cycle space methodology in complex geometry. Applications in various contexts are given. A significant portion of the book is devoted to material which is important in the general area of complex analysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of the book is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of the book. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction of the cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society.

Complex Analytic Cycles

Author : Daniel Barlet
Publisher :
ISBN 13 : 9783030311643
Total Pages : 545 pages
Book Rating : 4.3/5 (116 download)

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Book Synopsis Complex Analytic Cycles by : Daniel Barlet

Download or read book Complex Analytic Cycles written by Daniel Barlet and published by . This book was released on 2019 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of a presentation from scratch of cycle space methodology in complex geometry. Applications in various contexts are given. A significant portion of the book is devoted to material which is important in the general area of complex analysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of the book is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of the book. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction of the cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society.

Iterated Integrals and Cycles on Algebraic Manifolds

Author : Bruno Harris
Publisher : World Scientific
ISBN 13 : 9812562575
Total Pages : 121 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Iterated Integrals and Cycles on Algebraic Manifolds by : Bruno Harris

Download or read book Iterated Integrals and Cycles on Algebraic Manifolds written by Bruno Harris and published by World Scientific. This book was released on 2004 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This subject has been of great interest both to topologists and tonumber theorists. The first part of this book describes some of thework of Kuo-Tsai Chen on iterated integrals and the fundamental groupof a manifold. The author attempts to make his exposition accessibleto beginning graduate students. He then proceeds to apply Chen''sconstructions to algebraic geometry, showing how this leads to someresults on algebraic cycles and the AbelOCoJacobihomomorphism. Finally, he presents a more general point of viewrelating Chen''s integrals to a generalization of the concept oflinking numbers, and ends up with a new invariant of homology classesin a projective algebraic manifold. The book is based on a coursegiven by the author at the Nankai Institute of Mathematics in the fallof 2001."

Numerical Control over Complex Analytic Singularities

Author : David B. Massey
Publisher : American Mathematical Soc.
ISBN 13 : 0821832808
Total Pages : 268 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Numerical Control over Complex Analytic Singularities by : David B. Massey

Download or read book Numerical Control over Complex Analytic Singularities written by David B. Massey and published by American Mathematical Soc.. This book was released on 2003 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Milnor number is a powerful invariant of an isolated, complex, affine hyper surface singularity. It provides data about the local, ambient, topological-type of the hyper surface, and the constancy of the Milnor number throughout a family implies that Thom's $a_f$ condition holds and that the local, ambient, topological-type is constant in the family. Much of the usefulness of the Milnor number is due to the fact that it can be effectively calculated in an algebraic manner.The Le cycles and numbers are a generalization of the Milnor number to the setting of complex, affine hyper surface singularities, where the singular set is allowed to be of arbitrary dimension. As with the Milnor number, the Le numbers provide data about the local, ambient, topological-type of the hyper surface, and the constancy of the Le numbers throughout a family implies that Thom's $a_f$ condition holds and that the Milnor fibrations are constant throughout the family. Again, much of the usefulness of the Le numbers is due to the fact that they can be effectively calculated in an algebraic manner.In this work, we generalize the Le cycles and numbers to the case of hyper surfaces inside arbitrary analytic spaces. We define the Le-Vogel cycles and numbers, and prove that the Le-Vogel numbers control Thom's $a_f$ condition. We also prove a relationship between the Euler characteristic of the Milnor fibre and the Le-Vogel numbers. Moreover, we give examples which show that the Le-Vogel numbers are effectively calculable. In order to define the Le-Vogel cycles and numbers, we require, and include, a great deal of background material on Vogel cycles, analytic intersection theory, and the derived category. Also, to serve as a model case for the Le-Vogel cycles, we recall our earlier work on the Le cycles of an affine hyper surface singularity.

Carleman’s Formulas in Complex Analysis

Author : L.A. Aizenberg
Publisher : Springer Science & Business Media
ISBN 13 : 9401115966
Total Pages : 317 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Carleman’s Formulas in Complex Analysis by : L.A. Aizenberg

Download or read book Carleman’s Formulas in Complex Analysis written by L.A. Aizenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).

Le Cycles and Hypersurface Singularities

Author : David Massey
Publisher : Springer
ISBN 13 : 3540455213
Total Pages : 141 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Le Cycles and Hypersurface Singularities by : David Massey

Download or read book Le Cycles and Hypersurface Singularities written by David Massey and published by Springer. This book was released on 2006-11-14 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Lê cycles of the hypersurface. The Lê cycles and their multiplicities - the Lê numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Lê numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.

Algebraic Cycles and Hodge Theory

Author : Mark L. Green
Publisher : Springer
ISBN 13 : 3540490469
Total Pages : 276 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic Cycles and Hodge Theory by : Mark L. Green

Download or read book Algebraic Cycles and Hodge Theory written by Mark L. Green and published by Springer. This book was released on 2004-09-03 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

Polynomials and Vanishing Cycles

Author : Mihai Tibăr
Publisher : Cambridge University Press
ISBN 13 : 9780521829205
Total Pages : 284 pages
Book Rating : 4.8/5 (292 download)

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Book Synopsis Polynomials and Vanishing Cycles by : Mihai Tibăr

Download or read book Polynomials and Vanishing Cycles written by Mihai Tibăr and published by Cambridge University Press. This book was released on 2007-05-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations is proposed in this tract. Lefschetz theory, complex Morse theory and singularities of hypersurfaces are presented in detail leading to the latest research on topics such as the topology of singularities of meromorphic functions and non-generic Lefschetz pencils.

Numerical Control Over Complex Analytic Singularities

Author : Christopher Hart
Publisher :
ISBN 13 : 9781470403768
Total Pages : 268 pages
Book Rating : 4.4/5 (37 download)

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Book Synopsis Numerical Control Over Complex Analytic Singularities by : Christopher Hart

Download or read book Numerical Control Over Complex Analytic Singularities written by Christopher Hart and published by . This book was released on 2014-09-11 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview Part I. Algebraic Preliminaries: Gap Sheaves and Vogel Cycles: Introduction Gap sheaves Gap cycles and Vogel cycles The Le-Iomdine-Vogel formulas Summary of Part I Part II. Le Cycles and Hypersurface Singularities: Introduction Definitions and basic properties Elementary examples A handle decomposition of the Milnor fibre Generalized Le-Iomdine formulas Le numbers and hyperplane arrangements Thom's $a_f$ condition Aligned singularities Suspending singularities Constancy of the Milnor fibrations Another characterization of the Le cycles Part III. Isolated Critical Points of Functions on Singular Spaces: Introduction Critical avatars The relative polar curve The link between the algebraic and topological points of view The special case of perverse sheaves Thom's $a_f$ condition Continuous families of constructible complexes Part IV. Non-Isolated Critical Points of Functions on Singular Spaces: Introduction Le-Vogel cycles Le-Iomdine formulas and Thom's condition Le-Vogel cycles and the Euler characteristic Appendix A. Analytic cycles and intersections Appendix B. The derived category Appendix C. Privileged neighborhoods and lifting Milnor fibrations References Index.

Complex Geometry

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212904
Total Pages : 336 pages
Book Rating : 4.2/5 (129 download)

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Book Synopsis Complex Geometry by : Daniel Huybrechts

Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Le Cycles and Hypersurface Singularities

Author : David Massey
Publisher :
ISBN 13 : 9783662198391
Total Pages : 148 pages
Book Rating : 4.1/5 (983 download)

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Book Synopsis Le Cycles and Hypersurface Singularities by : David Massey

Download or read book Le Cycles and Hypersurface Singularities written by David Massey and published by . This book was released on 2014-09-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Transactions of the American Mathematical Society

Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 572 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Transactions of the American Mathematical Society by : American Mathematical Society

Download or read book Transactions of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1915 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.

Algebraic Cycles and Motives: Volume 2

Author : Jan Nagel
Publisher : Cambridge University Press
ISBN 13 : 0521701759
Total Pages : 360 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Algebraic Cycles and Motives: Volume 2 by : Jan Nagel

Download or read book Algebraic Cycles and Motives: Volume 2 written by Jan Nagel and published by Cambridge University Press. This book was released on 2007-05-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of the subject of algebraic cycles and motives as it stands.

Topology in Real-World Machine Learning and Data Analysis

Author : Kathryn Hess
Publisher : Frontiers Media SA
ISBN 13 : 2832504124
Total Pages : 229 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Topology in Real-World Machine Learning and Data Analysis by : Kathryn Hess

Download or read book Topology in Real-World Machine Learning and Data Analysis written by Kathryn Hess and published by Frontiers Media SA. This book was released on 2022-11-07 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis and Assessment of Cardiovascular Function

Author : Gary M. Drzewiecki
Publisher : Springer Science & Business Media
ISBN 13 : 9780387982823
Total Pages : 414 pages
Book Rating : 4.9/5 (828 download)

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Book Synopsis Analysis and Assessment of Cardiovascular Function by : Gary M. Drzewiecki

Download or read book Analysis and Assessment of Cardiovascular Function written by Gary M. Drzewiecki and published by Springer Science & Business Media. This book was released on 1998 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of cardiovascular function is vital to contemporary biomedical research. However, integration between cellular and subcellular research and organ-level studies is often lacking, as is integration of clinical and basic investigation. This book examines cardiovascular system function from the perspectives of assessment and analysis, with a focus on evaluating function at different anatomical levels using a combination of analytical, experimental, and clinical measurements.

The Collected Papers Of Wei-liang Chow

Author : Shiing-shen Chern
Publisher : World Scientific
ISBN 13 : 9814487937
Total Pages : 522 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis The Collected Papers Of Wei-liang Chow by : Shiing-shen Chern

Download or read book The Collected Papers Of Wei-liang Chow written by Shiing-shen Chern and published by World Scientific. This book was released on 2002-09-23 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow's name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow's theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow's theorem — that a compact analytic variety in a projective space is algebraic — is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911-95) as a mathematician began in China with professorships at the National Central University in Nanking (1936-37) and the National Tung-Chi University in Shanghai (1946-47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977.