Lectures On Surfaces
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Lectures On Surfaces
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Author : A. B. Katok
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Surfaces written by A. B. Katok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
Lectures On K3 Surfaces
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26
Lectures On K3 Surfaces written by Daniel Huybrechts 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 2016-09-26 with Mathematics categories.
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Lectures On Curves Surfaces And Projective Varieties
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Author : Mauro Beltrametti
language : en
Publisher: European Mathematical Society
Release Date : 2009
Lectures On Curves Surfaces And Projective Varieties written by Mauro Beltrametti and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems
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Author : Johannes C. C. Nitsche
language : en
Publisher:
Release Date : 1989
Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems written by Johannes C. C. Nitsche 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.
This book is a revised and translated version of the first five chapters of Vorlesungen ^D"uber Minimalfl^D"achen. It deals with the parametric minimal surface in Euclidean space. The author presents a broad survey that extends from the classical beginnings to the current situation while highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks.
Lectures On Curves On An Algebraic Surface
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Author : David Mumford
language : en
Publisher: Princeton University Press
Release Date : 1966-08-21
Lectures On Curves On An Algebraic Surface written by David Mumford 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 1966-08-21 with Mathematics categories.
These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
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.
Lectures On Hilbert Schemes Of Points On Surfaces
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Author : Hiraku Nakajima
language : en
Publisher: American Mathematical Soc.
Release Date :
Lectures On Hilbert Schemes Of Points On Surfaces written by Hiraku Nakajima and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The Hilbert scheme $X{[n] $ of a surface $X$ describes collections of $n$ (not necessarily distinct) points on $X$. More precisely, it is the moduli space for $0$-dimensional subschemes of $X$ of length $n$. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory-even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. For example, a construction of the representation of the infinite dimensional Heisenberg algebra (i.e., Fock space) is presented. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field theory, etc. However, the construction presented in this volume is completely unique and provides the unexplored link between geometry and representation theory. The book offers a nice survey of current developments in this rapidly growing subject. It is suitable as a text at the advanced graduate level.
Lectures On Vector Bundles Over Riemann Surfaces
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Author : Robert C. Gunning
language : en
Publisher: Princeton University Press
Release Date : 1967-11-21
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 1967-11-21 with Mathematics categories.
The description for this book, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6, will be forthcoming.
Lectures On Riemann Surfaces
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Author : Robert C. Gunning
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Lectures On 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 2015-03-08 with Mathematics categories.
A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. 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.
Mostly Surfaces
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Author : Richard Evan Schwartz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Mostly Surfaces written by Richard Evan Schwartz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.