Basic Algebraic Geometry, Volume 2The second volume of Shafarevich's introductory book on algebraic varieties and complex manifolds. As with Volume 1, the author has revised the text and added new material, e.g. as 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 those in theoretical physics. |
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1-dimensional complex 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 components connected consider constructed coordinates corresponding defined definition degree denoted differential form dimension divisor elements elliptic curves embedding equation example exists fibre field follows given Hence Hermitian Hilbert polynomial holomorphic functions homomorphism integrals intersection invariant inverse image irreducible isomorphic Kähler metric lemma line bundle linear matrix maximal ideal meromorphic functions modules morphism neighbourhood Noetherian nonsingular projective curve notion obviously open sets orientation parameters presheaf prime ideal projective variety proof properties Proposition prove quotient rational function restriction Riemann ringed space satisfying sheaf F sheaves simplex Spec submanifold subset subspace subvariety Suppose surface tangent space Theorem topological space torus triangulation U₁ V₁ vector bundle vector space write