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Author: Martin Schlichenmaier
Publisher: Springer Science & Business Media
ISBN: 3540711759
Category : Science
Languages : en
Pages : 217
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Book Description
This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
Author: Martin Schlichenmaier
Publisher: Springer Science & Business Media
ISBN: 3540711759
Category : Science
Languages : en
Pages : 217
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Book Description
This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
Author: Martin Schlichenmaier
Publisher: Springer
ISBN: 9783662137284
Category : Mathematics
Languages : en
Pages : 149
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Book Description
This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.
Author: Benson Farb
Publisher: American Mathematical Soc.
ISBN: 0821898876
Category : Mathematics
Languages : en
Pages : 371
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Book Description
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author: S. M. Natanzon
Publisher: American Mathematical Soc.
ISBN: 9780821889657
Category : Mathematics
Languages : en
Pages : 172
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Book Description
The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. This book focuses on the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, and the space of mappings.
Author: Lizhen Ji
Publisher:
ISBN: 9781571463531
Category : Geometry, Algebraic
Languages : en
Pages : 232
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Book Description
The concept of Riemann surfaces was introduced in Riemann's thesis, and the moduli space of Riemann surfaces was defined by Riemann in a masterpiece a few years later. Due to a broad connection with many subjects in mathematics and physics, Riemann surfaces and their moduli spaces have been intensively studied and should continue to attract attention in years to come. Recently, there has been an explosion of interest in and work on tropical algebraic curves--analogues of algebraic curves over the complex numbers and hence of Riemann surfaces. This book is an accessible introduction to all these topics, with special emphasis given to their many connections with subjects such as algebraic geometry, complex analysis, hyperbolic geometry, topology, geometric group theory, and mathematical physics.
Author: M. Seppälä
Publisher: Elsevier
ISBN: 9780080872803
Category : Mathematics
Languages : en
Pages : 262
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Book Description
The moduli problem is to describe the structure of the space of isomorphism classes of Riemann surfaces of a given topological type. This space is known as the moduli space and has been at the center of pure mathematics for more than a hundred years. In spite of its age, this field still attracts a lot of attention, the smooth compact Riemann surfaces being simply complex projective algebraic curves. Therefore the moduli space of compact Riemann surfaces is also the moduli space of complex algebraic curves. This space lies on the intersection of many fields of mathematics and may be studied from many different points of view. The aim of this monograph is to present information about the structure of the moduli space using as concrete and elementary methods as possible. This simple approach leads to a rich theory and opens a new way of treating the moduli problem, putting new life into classical methods that were used in the study of moduli problems in the 1920s.
Author: Renzo Cavalieri
Publisher: Cambridge University Press
ISBN: 110714924X
Category : Mathematics
Languages : en
Pages : 197
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Book Description
Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
Author: Lizhen Ji
Publisher:
ISBN: 9787040474190
Category : Geometry, Algebraic
Languages : en
Pages : 221
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Book Description
Author: Maxim E. Kazaryan
Publisher: Springer
ISBN: 3030029433
Category : Mathematics
Languages : en
Pages : 231
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Book Description
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework
Author: Maurizio Cornalba
Publisher: World Scientific
ISBN: 9814590878
Category : Mathematics
Languages : en
Pages : 716
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Book Description
