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Other titles in the Theoretical and Mathematical Physics series:
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces (Theoretical and Mathematical Physics)by Martin Schlichenmaier
Synopses & Reviews
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.
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.
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