Basic Algebraic Geometry 2The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics. |
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Abelian affine scheme affine variety algebraic curve algebraic variety analytic functions arbitrary automorphism blowup Chap closed point closed subscheme coherent sheaf compact complex complex manifold complex space condition connected consider constructed coordinates corresponding defined definition degree denoted differential form dimension divisor elements elliptic curves equation example exists fibre field finite follows geometry given Hence Hermitian Hilbert polynomial holomorphic functions homomorphism integrals intersection invariant inverse image irreducible isomorphic Kähler metric lemma line bundle linear linearly maximal ideal meromorphic functions modules neighbourhood Noetherian notion obviously open sets parameters presheaf prime ideal projective variety proof properties Proposition prove quasiprojective varieties quotient rational function restriction Riemann ringed space satisfying sheaf F sheaves Spec subspace subvariety Suppose surface tangent space Theorem theory topological space torus triangulation U₁ universal cover V₁ vector bundle vector space write
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Page 254 - Elementary theory of analytic functions of one or several complex variables, Hermann, Paris 1963 and Addison Wesley, Reading, Mass., Palo Alto, London 1963; MR 26 #5138.
Page 255 - Kawamata, Y.; Matsuda, K.; Matsuki, K.: Introduction to the minimal model problem.