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 Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
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2-plane Abelian variety algebraic variety analytic subvariety analytic variety automorphism base locus base points blow-up canonical curve Chapter Chern class codimension cohomology complex manifold compute conic containing corresponding cubic curvature decomposition defined denote differential dimension disjoint double points dual duality effective divisor elliptic surface embedding exact sequence exceptional divisor fiber follows genus g geometry given gives Grassmannian hence hermitian Hodge holomorphic function holomorphic map homology hyperplane section hypersurface integral intersection number inverse image irreducible isomorphism Kodaira l-form Lefschetz lemma line bundle linear system linearly locus map f matrix meet meromorphic function metric multiple neighborhood nondegenerate nonzero Note open set pencil plane polynomial positive projection map projective space Proof proper transform prove pullback quadric quotient rational normal curve residue Riemann surface Riemann-Roch Schubert cycle sheaf sheaves singular point span spectral sequence subspace Suppose surface of genus surjective tangent line theorem transversely trivial vanishing Weierstrass write zero