Lectures On Vector Bundles Over Riemann Surfaces

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Lectures On Vector Bundles Over Riemann Surfaces

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Author : Robert C. Gunning
language : en
Publisher: Princeton University Press
Release Date : 2020-09-01

Lectures On Vector Bundles Over Riemann Surfaces written by Robert C. Gunning and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.

These notes are based on a course of lectures given at Princeton University during the academic year 1966–1967. The topic is the analytic theory of complex vector bundles over compact Riemann surfaces. It begins with a general discussion of complex analytic vector bundles over compact Riemann surfaces from the point of view of sheaf theory. It goes on to discuss a descriptive classification of complex analytic vector bundles of rank 2 on a compact Riemann surface and follows with a discussion of flat vector bundles over compact Riemann surfaces. Two appendices cover some questions that arise.

Lectures On Vector Bundles Over Riemann Surfaces Preliminary Informal Notes Of University Courses And Seminars In Mathematics

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Author :
language : en
Publisher:
Release Date :

Lectures On Vector Bundles Over Riemann Surfaces Preliminary Informal Notes Of University Courses And Seminars In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Lectures On Vector Bundles Over Riemann Surfaces

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Author : R.C. Gunning
language : it
Publisher:
Release Date : 1967

Lectures On Vector Bundles Over Riemann Surfaces written by R.C. Gunning and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Lectures On Vector Bundles Over Riemann Surfaces

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Author : Robert Clifford Gunning (Mathematician, United States)
language : en
Publisher:
Release Date : 1967

Lectures On Vector Bundles Over Riemann Surfaces written by Robert Clifford Gunning (Mathematician, United States) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Lectures On Vector Bundles

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Author : J. Le Potier
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-28

Lectures On Vector Bundles written by J. Le Potier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-28 with Mathematics categories.

This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Riemann Surfaces And Generalized Theta Functions

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Author : Robert C. Gunning
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Riemann Surfaces And Generalized Theta Functions written by Robert C. Gunning and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.

Lectures On Riemann Surfaces

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Author : Maurizio Cornalba
language : en
Publisher:
Release Date : 1989

Lectures On Riemann Surfaces written by Maurizio Cornalba and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

The first College on Riemann Surfaces centered on the theory of Riemann surfaces and their moduli and its applications to physics. This volume contains revised versions of the notes distributed at the College.

Interpolation Theory Systems Theory And Related Topics

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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Interpolation Theory Systems Theory And Related Topics written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Geometric Study Of Foliations Proceedings Of The International Symposium Workshop

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Author : Tadayoshi Mizutani
language : en
Publisher: World Scientific
Release Date : 1994-12-16

Geometric Study Of Foliations Proceedings Of The International Symposium Workshop written by Tadayoshi Mizutani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-16 with categories.

This book covers recent topics in various aspects of foliation theory and its relation with other areas including dynamical systems, C∗-algebras, index theory and low-dimensional topology. It contains survey articles by G Hector, S Hurder and P Molino, as well as more than 20 original papers by specialists who are currently most active in the field.

Geometry Of Vector Sheaves

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Author : Anastasios Mallios
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Geometry Of Vector Sheaves written by Anastasios Mallios and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

This text is part of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.