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Zariski surfaces

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Rozprawy Matematyczne tom/nr w serii: 200 wydano: 1983
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CONTENTS
Acknowledgements...................................................................................................5
Introduction..............................................................................................................6
Notations..................................................................................................................8
Chapter I. Zariski surfaces: definition and general properties................................10
Chapter II. The theory of adjoints..........................................................................14
  Introduction..........................................................................................................14
  §1. Behaviour of $ω_X$ under restriction to open subschemes............................15
  §2. Behaviour of $ω_X$ under certain birational maps..........................................16
  §3. Affine case, adjoints........................................................................................16
  §4. Projective case................................................................................................20
  §5. Theory of l-adjoints for l ≥ 1 (an outline).........................................................24
  §6. Valuation theory for differentials.....................................................................25
Chapter III. An example relating to a question of O. Zariski...................................28
  Introduction..........................................................................................................28
  Part 1. Equation of the surface, singularities in characteristic 2..........................29
  Part 2. .................................................................................................................33
  Part 3. The singularity of F̅ at infinity....................................................................44
    §1. Introductory remarks...................................................................................45
    §2. Resolution of the singularity at infinity.........................................................47
    §3. Behaviour of differentials at infinity under the resolution.............................52
  Part 4. Conclusion................................................................................................57
  Part 5. Appendix...................................................................................................58
Chapter IV. Generic Zariski surfaces..........................................................................64
Chapter V. Richness of the class of Zariski surfaces.................................................76
References................................................................................................................80
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 200
Liczba stron
81
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CC
Daty
wydano
1983
Twórcy
autor
Bibliografia
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  • [Bl] P. Blass, Zariski Surfaces, Thesis, University of Michigan, 1977.
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  • [Lang] W. E. Lang, Quasi-elliptic surfaces in characteristic three, Thesis, Harvard University, 1978.
  • [Li] J. Lipman, Rational Singularities, IHES, Publications, No. 36.
  • [Mi 1] J. S. Milne, Étale cohomology, Princeton University Press, 1966.
  • [Mi 2] J. S. Milne, Duality in the flat cohomology of a surface, Ann. Sci. Éc. Norm. Sup. 4e serie, t. 9, 1976, p. 171-202, Theorem 4.5.
  • [Mu 1] D. Mumford, Lectures on curves on an algebraic surface, Ann. of Math. Studies, No. 59, Princeton University Press (1966).
  • [Mu 2] D. Mumford, Introduction to algebraic geometry (Preliminary version of the first 3 chapters), Harvard Lecture Notes, p. 335.
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  • [Ša 1] I. Šafarevič, Minimal Models, Tata Institute of Fundamental Research, Bombay 1966.
  • [Ša 2] I. Šafarevič, Proceedings of the Steklov, Institute of Mathematics 75 (1965); AMS, Providence, Rhode Island (English translation of [Ša 3]).
  • [Ša 3] I. Šafarevič, Algebraic surfaces, Steklov Institute, Proceedings, Vol. 75 (1965).
  • [Ša 4] I. Šafarevič, Basic Algebraic Geometry, Springer, 1974.
  • [Se] J. P. Serre, Faisceaux algébrique coherent, Ann. of Math. 61 (1955), pp. 197-278.
  • [Sh] T. Shioda, An example of unirational surfaces in characteristic P, Math. Ann. 211 (1974), p. 233 -236.
  • [Za 1] O. Zariski, Introduction to the problem of minimal models in the theory of algebraic surfaces, Publ. Math. Soc. Japan 4 (1958).
  • [Za 2] O. Zariski, The problem of minimal models in the theory of algebraic surfaces, Amer. J. Math. 80 (1958), p. 153.
  • [Za 3] O. Zariski, On Castelnuovo's Criterion of Rationality $p_a = P_2 = 0$ of an algebraic surface, III. J. Math. 2 (3) (1958), p. 303 (especially p. 314).
  • [Za 4] O. Zariski, Introduction to the theory of algebraic surfaces. Lecture Notes in Mathematics 83, Springer.
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0012-3862
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