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An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
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Paperback
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Artikel-Nr:
9783642090271
Veröffentl:
2010
Einband:
Paperback
Erscheinungsdatum:
30.11.2010
Seiten:
236
Autor:
Martin Schlichenmaier
Gewicht:
365 g
Format:
235x155x13 mm
Serie:
Theoretical and Mathematical Physics
Sprache:
Englisch
Beschreibung:
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.
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.
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.