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Algebraic Geometry by Alexei Skorobogatov

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Algebraic Geometry written by Alexei Skorobogatov . This is an other book of mathematics cover the following topics.

  • Basics of commutative algebra
    Integral closure. Noetherian rings, Noether’s normalization and Nullstellensatz

  • Affine geometry
    Zariski topology, Category of affine varieties, Examples of rational varieties, Smooth and singular points, Dimension. Application: Tsen’s theorem

  • Projective geometry
    Projective varieties, Morphisms of projective varieties

  • Local geometry
    Localization, local rings, DVR, Regular local rings, Geometric consequences of unique factorization in OP

  • Divisors
    The Picard group, Automorphisms of Pnk and of Ank, The degree of the divisor of a rational function on a projective curve, Bezout theorem for curves, Riemann–Roch theorem, From algebraic curves to error correcting codes

  • A More algebra
    Krull’s intersection theorem, Completion, The topological space Spec(R)

  • B More geometry
    Finite morphisms, Functoriality of Pic

  • Download free PDF Algebraic Geometry by Alexei Skorobogatov
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