Book Volume 83 1969

An Introduction to the Theory of Algebraic Surfaces

Notes by James Cohn, Harvard University, 1957–58

Authors:

ISBN: 978-3-540-04602-8 (Print) 978-3-540-36092-6 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages I-V

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    Chapter

    Pages 1-3

    Homogeneous and non-homogeneous point coordinates

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    Chapter

    Pages 3-4

    Coordinate rings of irreducible varieties

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    Chapter

    Pages 4-5

    Normal varieties

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    Chapter

    Pages 6-11

    Divisorial cycles on a normal projective variety V/k (dim(V)=r≥1)

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    Chapter

    Pages 11-15

    Linear systems

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    Chapter

    Pages 15-19

    Divisors on an arbitrary variety V

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    Chapter

    Pages 19-23

    Intersection theory on algebraic surfaces (k algebraically closed)

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    Chapter

    Pages 24-28

    Differentials

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    Chapter

    Pages 29-34

    The canonical system on a variety V

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    Chapter

    Pages 34-48

    Trace of a differential

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    Chapter

    Pages 49-51

    The arithemetic genus

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    Chapter

    Pages 52-62

    Normalization and complete systems

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    Chapter

    Pages 63-71

    The Hilbert characteristic function and the arithmetic genus of a variety

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    Chapter

    Pages 72-80

    The Riemann-Roch theorem

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    Chapter

    Pages 80-95

    Subadjoint polynomials

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    Chapter

    Pages 95-100

    Proof of the fundamental lemma