An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

Softcover version of original hardcover Auflage 2007
ISBN: 978-3-642-09027-1
Verlag: Springer

Buch, Englisch, 217 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 365 g

Reihe: Theoretical and Mathematical Physics

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Schlichenmaier, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.