Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves
Author: Lizhen Ji
Publisher:
Published: 2017
Total Pages: 221
ISBN-13: 9787040474190
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An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
Author: Martin Schlichenmaier
Publisher: Springer Science & Business Media
Published: 2010-02-11
Total Pages: 228
ISBN-13: 3540711759
DOWNLOAD EBOOK →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.
An Introduction to Families, Deformations and Moduli
Author: Thiruvalloor E. Venkata Balaji
Publisher: Universitätsverlag Göttingen
Published: 2010
Total Pages: 241
ISBN-13: 3941875329
DOWNLOAD EBOOK →Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.
Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs
Author: S. M. Natanzon
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 160
ISBN-13: 9780821835944
DOWNLOAD EBOOK →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. The present book is devoted to the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, the space of mappings, and also superanalogs of all these spaces. The book can be used by researchers and graduate students working in algebraic geometry, topology, and mathematical physics.
Moduli Spaces of Riemann Surfaces
Author: Benson Farb
Publisher: American Mathematical Soc.
Published: 2013-08-16
Total Pages: 371
ISBN-13: 0821898876
DOWNLOAD EBOOK →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.
Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces
Author: Maurizio Cornalba
Publisher: World Scientific
Published: 1989-06-01
Total Pages: 716
ISBN-13: 9814590878
DOWNLOAD EBOOK →Geometry of Riemann Surfaces and Teichmüller Spaces
Author: Mika Seppälä
Publisher: North Holland
Published: 1992
Total Pages: 263
ISBN-13: 9780444888464
DOWNLOAD EBOOK →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.
Mapping Class Groups and Moduli Spaces of Riemann Surfaces
Author: Carl-Friedrich Bödigheimer
Publisher: American Mathematical Soc.
Published: 1993
Total Pages: 396
ISBN-13: 9780821854846
DOWNLOAD EBOOK →The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.
Riemann Surfaces and Algebraic Curves
Author: Renzo Cavalieri
Publisher: Cambridge University Press
Published: 2016-09-26
Total Pages: 197
ISBN-13: 1316798933
DOWNLOAD EBOOK →Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Moduli Spaces of Riemann Surfaces
Author: Benson Farb
Publisher:
Published: 2013
Total Pages: 356
ISBN-13: 9781470409944
DOWNLOAD EBOOK →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 g.
