Principles of Algebraic Geometry
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of...
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A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
Ch. 0Foundational Material11Rudiments of Several Complex Variables2Complex Manifolds3Sheaves and Cohomology4Topology of Manifolds5Vector Bundles, Connections, and Curvature6Harmonic Theory on Compact Complex Manifolds7Kahler ManifoldsCh. 1Complex Algebraic Varieties1281Divisors and Line Bundles2Some Vanishing Theorems and Corollaries3Algebraic Varieties4The Kodaira Embedding Theorem5GrassmanniansCh. 2Riemann Surfaces and Algebraic Curves2121Preliminaries2Abel's Theorem3Linear Systems on Curves4Plucker Formulas5Correspondences6Complex Tori and Abelian Varieties7Curves and Their JacobiansCh. 3Further Techniques3641Distributions and Currents2Applications of Currents to Complex Analysis3Chern Classes4Fixed-Point and Residue Formulas5Spectral Sequences and ApplicationsCh. 4Surfaces4691Preliminaries2Rational Maps3Rational Surfaces I4Rational Surfaces II5Some Irrational Surfaces6Noether's FormulaCh. 5Residues6471Elementary Properties of Residues2Applications of Residues3Rudiments of Commutative and Homological Algebra with Applications4Global DualityCh. 6The Quadric Line Complex7331Preliminaries: Quadrics2The Quadric Line Complex: Introduction3Lines on the Quadric Line Complex4The Quadric Line Complex: RepriseIndex805
