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Author: Hong-Jong Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 130
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Book Description
Author: Hong-Jong Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 130
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Book Description
Author: Shoshichi Kobayashi
Publisher: Princeton University Press
ISBN: 1400858682
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Vasile Brinzanescu
Publisher: Springer
ISBN: 3540498451
Category : Mathematics
Languages : en
Pages : 175
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Book Description
The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.
Author: Bo Berndtsson
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: Jeffery D. McNeal
Publisher: American Mathematical Soc.
ISBN: 0821872753
Category : Mathematics
Languages : en
Pages : 601
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Book Description
"Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the 'other side' of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists."--Publisher's description.
Author: Angelynn Reario Alvarez
Publisher:
ISBN:
Category : Complex manifolds
Languages : en
Pages :
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Book Description
In complex geometry, there are few known examples of, and few known results about, manifolds with metrics of positive curvature. For instance, the geometry of fiber bundles and total spaces of fibrations over positively-curved complex manifolds is mysterious and not well-understood. In this dissertation, we study the existence of (pinched) metrics of positive curvature on a particular type of fiber bundle---namely metrics of positive holomorphic sectional curvature on projectivized vector bundles over compact complex manifolds. We first prove a general theorem for projectivized vector bundles, then we discuss a curvature pinching result for projectivized rank 2 vector bundles over complex projective space of dimension 1.
Author: Michele Audin
Publisher: Birkhäuser
ISBN: 3034885083
Category : Mathematics
Languages : en
Pages : 333
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Book Description
This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.
Author: Samuel I. Goldberg
Publisher: Courier Corporation
ISBN: 048640207X
Category : Mathematics
Languages : en
Pages : 417
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Book Description
This systematic and self-contained treatment examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. It generalizes the theory of Riemann surfaces to that of Riemannian manifolds. Includes four helpful appendixes. "A valuable survey." — Nature. 1962 edition.
Author: Chris Wendl
Publisher: Springer
ISBN: 3319913719
Category : Mathematics
Languages : en
Pages : 303
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Book Description
This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Author: Taejung Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 104
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Book Description
The work by N. Hitchin in 1987 opened a good possibility of describing the cotangent bundle of the moduli space of stable vector bundles over a compact Riemann surface reals in an explicit way. In [32], he proved that the space can be foliated by a family of certain spaces, i.e., the Jacobi varieties of spectral curves. The main purpose of this dissertation is to make the realization of the Hitchin system in a concrete way in the method initiated by I. M. Krichever in [44] and to give the necessary and sufficient condition for the linearity of flows in a Lax representation in terms of cohomological classes using the similar technique and analysis from the work by P. A. Griffiths in [27].
