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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.
List 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.
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.
Summary
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.
Additional text
From the reviews of the second edition:
"As the title suggests, this book is an introduction to Riemann surfaces, with the target audience being students of string theory. … an excellent book to use to become familiar with these concepts, and as a result the book is able to touch on a wide variety of concepts which are not broached by more traditional treatments of the subject. … I would certainly recommend the book for anyone who wants an enjoyable conceptual introduction to what can be a highly technical subject." (Mark Gross, Mathematical Reviews, Issue 2008 k)
"This book is an introduction to the language of modern algebraic geometry, designed mainly for Physics students who are interested in string theory. … Overall the book is very readable and it fulfills its goal remarkably well … that are useful to physicists interested in string theory, with all the necessary references for further reading. This book will be an excellent addition to the bookshelf of any physics student or researcher who wants to learn about the mathematical aspects of string theory." (Valentino Tosatti, Zentrablatt MATH, Vol. 1153, 2009)
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From the reviews of the second edition:
"As the title suggests, this book is an introduction to Riemann surfaces, with the target audience being students of string theory. ... an excellent book to use to become familiar with these concepts, and as a result the book is able to touch on a wide variety of concepts which are not broached by more traditional treatments of the subject. ... I would certainly recommend the book for anyone who wants an enjoyable conceptual introduction to what can be a highly technical subject." (Mark Gross, Mathematical Reviews, Issue 2008 k)
"This book is an introduction to the language of modern algebraic geometry, designed mainly for Physics students who are interested in string theory. ... Overall the book is very readable and it fulfills its goal remarkably well ... that are useful to physicists interested in string theory, with all the necessary references for further reading. This book will be an excellent addition to the bookshelf of any physics student or researcher who wants to learn about the mathematical aspects of string theory." (Valentino Tosatti, Zentrablatt MATH, Vol. 1153, 2009)
