An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
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 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 - the modern language and modern view of Algebraic Geometry, and Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture.

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An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
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 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 - the modern language and modern view of Algebraic Geometry, and Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture.

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An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

by Martin Schlichenmaier
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

by Martin Schlichenmaier

Overview

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 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 - the modern language and modern view of Algebraic Geometry, and Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture.

Product Details

ISBN-13: 9783540711742
Publisher: Springer Berlin Heidelberg
Publication date: 08/21/2007
Series: Theoretical and Mathematical Physics
Edition description: 2nd ed. 2007
Pages: 217
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

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

Manifolds.- Topology of Riemann Surfaces.- Analytic Structure.- Diffierentials 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.- TopoModern Algebraic Geometry.- Schemes.- Hodge Decomposition and K¨ahler Manifold.- Calabi-Yau Manifolds and Mirror Symmetry.
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