Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
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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.
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.
