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An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces (Theoretical and Mathematical Physics)

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Synopses & Reviews

Publisher Comments:

This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role nowadays in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches. At the end of each chapter suggestions for further reading are given to allow the reader to study the touched topics in greater detail. This second edition of the book contains two additional more advanced geometric techniques: (1) The modern language and modern view of Algebraic Geometry and (2) Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture. Graduate students of theoretical and mathematical physics will appreciate this book as textbook. Students of mathematics who are looking for a short introduction to the various aspects of modern geometry and their interplay will also find it useful. Researchers will esteem the book as reliable reference.

Synopsis:

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.

About the Author

Martin Schlichenmaier is full professor for mathematics at the University of  Luxemburg. He has held several teaching and research positions in the mathematics department of the University of Mannheim.

Table of Contents

Introduction.- Manifolds.- Topology of Riemann Surfaces.- Analytic Structure.- Differentials and Integration.- Tori and Jacobians.- Projective Varieties.- Moduli Spaces of Curves.- Vector Bundles, Sheaves and Cohomology.- The Theorem of Riemann-Roch for Line Bundles.- The Mumford Isomorphism on the Moduli Space.- Modern Algebraic Geometry.- Schemes.- Hodge Decomposition and Kähler Manifold.- Calabi-Yau Manifolds and Mirror Symmetry.

Product Details

ISBN:
9783540711742
Author:
Schlichenmaier, Martin
Publisher:
Springer
Subject:
Mathematical Physics
Subject:
Topology - General
Subject:
Nuclear Physics
Subject:
Algebraic Geometry
Subject:
Applications of Geometry in String Theory
Subject:
Mirror symmetry.
Subject:
moduli spaces
Subject:
Riemann surfaces
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Elementary Particles, Quantum Field Theory
Subject:
Algebraic Topology <P>This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role today in contemporary theoretical physics. He presents various techniques
Subject:
Physics-Math
Subject:
Algebraic topology
Copyright:
Edition Number:
2
Edition Description:
2nd ed. 2007
Series:
Theoretical and Mathematical Physics
Publication Date:
20071004
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
234
Dimensions:
235 x 155 mm 1120 gr

Related Subjects

Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Topology
Science and Mathematics » Physics » Math
Science and Mathematics » Physics » Nuclear

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces (Theoretical and Mathematical Physics) New Hardcover
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Product details 234 pages Springer - English 9783540711742 Reviews:
"Synopsis" by , 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.
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