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Tytuł książki

Zariski surfaces

Autorzy

Piotr Blass

Seria

Rozprawy Matematyczne tom/nr w serii: 200 wydano: 1983

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Pełne teksty:
rm20001.pdf

Warianty tytułu

Abstrakty

EN

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

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

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
Piotr Blass

Bibliografia

  • [Ab] S. S. Abhyankar, Local uniformation on algebraic surfaces over ground fields of characteristic p ≠ 0, Ann. of Math. 63 (19), pp. 491-526.
  • [Ar] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), p. 129.
  • [BH] E. Bombieri and D. Husemoller, Classification and embeddings of surfaces. Proceedings of Symposia in Pure Mathematics, Vol. 29, Arcata 1974, p. 373 (table).
  • [Bo] E. Bombieri, Canonical models of surfaces of general type, IHES Publications, No. 42, Theorem 1, p. 173.
  • [Bl] P. Blass, Zariski Surfaces, Thesis, University of Michigan, 1977.
  • [BL] P. Blass and J. Lipman, Remarks on adjoints and arithmetic genera of algebraic varieties, Amer. J. Math. 101 (2) (1979), pp. 331-336.
  • [De] P. Deligne, La Conjecture de Weil, I, Publ. Math. IHES 43 (1974), pp. 273-307.
  • [En 1] F. Enriques, Le superficie Algebriche, Nicola Zanichelli Editore, Bologna 1949.
  • [En 2] F. Enriques, Sopra Le Superficie Algebriche di Bigenere uno, Memoria Scelte Di Geometria, Vol. 2, p. 241.
  • [GR] H. Grauert and O. Riemenschneider, Verschwindungssätze für analytische Kohomologie-gruppen auf komplexen Räumen, Inventiones Math. 11 (4) (1970), p. 271.
  • [Ha] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer Verlag, New York-Heidelberg-Berlin 1977.
  • [La] S. Lang, Abelian Varieties, Interscience Tracts, in Pure and Applied Mathematics, No. 7, New York.
  • [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.
  • [Na] M. Nagata, Local Rings, Interscience tracts in Pure and Applied Mathematics 13.
  • [Nak] Y. Nakai, On the characteristic linear systems of algebraic families. III. J. Math. 1 (1957), pp. 552-561.
  • [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.

Języki publikacji

EN

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Identyfikator YADDA

bwmeta1.element.zamlynska-59b51417-2a71-4ed6-a74b-f7430b1c8f7a

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ISBN
83-01-01971-9
ISSN
0012-3862

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DML-PL
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