Principles of Algebraic GeometryA 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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2plane algebraic analytic varieties automorphism blowup bythe canonical curve Chern class cohomology compact complex manifold compute conic containing coordinates corresponding cubic decomposition defined degree denote dimension double points dual elliptic Enriques surface exact sequence exceptional divisor fiber finite formula geometry given by images global Grassmannian hence hermitian holomorphic function hyperplane section hypersurface images and images images i.e. images images intersection number inthe irreducible isomorphism isthe Kähler Kodaira Lefschetz lemma let images line bundle linear system locus map images matrix meromorphic function metric multiplicity neighborhood nondegenerate nonzero Note ofthe pencil plane Poincaré polynomial projection Proof proper transform prove pullback quadric rational rational normal curve residue Riemann surface RiemannRoch Schubert cycle selfintersection sequence images sheaf sheaves singular smooth space subspace Suppose tangent theorem transversely trivial vanishing vector bundle wehave welldefined write images zero