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On the existence of some surfaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1417)

Keywords

  • Line Bundle
  • Minimal Model
  • Projective Surface
  • Sectional Genus
  • Hyperplane Section

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Beltrametti M., Biancofiore A. and Sommese A.J., Projective N-folds of Log General Type, I. To appear on Trans. Amer.Math.Soc.

    Google Scholar 

  2. Bese E., On the spannedness and very ampleness of certain line bundles on the blow-ups of P 2 and F1. Math.Ann.262,225–238(1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Biancofiore A., On the hyperplane sections of blow-ups of complex projective plane. To appear on Can.J.Math.

    Google Scholar 

  4. Biancofiore A., On the hyperplane sections of ruled surfaces. Preprint

    Google Scholar 

  5. Biancofiore A. and Livorni E.L., On the iteration of the adjunction process in the study of rational surfaces. Ind. Univ. Math. J. Vol 36,No.1,167–188(1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Biancofiore A. and Livorni E.L., Algebraic non-ruled surfaces with sectional genus equal to seven. Ann. Univ. Ferrara. Sez.VII-Sc. Mat. Vol. XXXII,1–14(1986).

    MathSciNet  MATH  Google Scholar 

  7. Biancofiore A. and Livorni E.L., On the iteration of the adjunction process for surfaces of negative Kodaira dimension. To appear on Manuscripta Mathematica.

    Google Scholar 

  8. Biancofiore A. and Livorni E.L., On the genus of a hyperplane section of a geometrically ruled surface. Annali di Matematica pura ed applicata (IV), Vol. CXLVII,173–185(1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Buium A., On surfaces of degree at most 2n+1 in P n. Proceedings of the week of algebraic geometry, Bucharest 1982. Lect.Notes Math. Vol.1056. Berlin, Heidelberg, New York. Springer 47–60 (1984).

    MATH  Google Scholar 

  10. Castelnuovo G., Sulle superficie algebriche le cui sezioni piane sono curve iperellittiche. Memorie Scelte, XII, Zanichelli, Bologna (1939).

    MATH  Google Scholar 

  11. Castelnuovo G., Sulle superficie algebriche le cui sezioni sono curve di genere 3. Memorie Scelte, XIII, Zanichelli, Bologna (1939).

    MATH  Google Scholar 

  12. Castelnuovo G. and Enriques F., Sur quelques resultats nouveaux dans la theorie des surfaces algebrique. Note V in [30] below.

    Google Scholar 

  13. Comessatti A., Sulle superficie di Jacobi semplicemente singolari. Mem.Soc.Ital. delle Scienze (deiXL) (3)21, 45–71(1919).

    Google Scholar 

  14. Griffiths P.A. and Harris J., Principles of Algebraic Geometry. A. Wiley-Interscience publication, (1978)

    Google Scholar 

  15. Hartshorne R., Algebraic Geometry. Springer Verlag, New York (1977).

    CrossRef  MATH  Google Scholar 

  16. Harris J., A bound on the geometric genus of projective varieties. Ann.Scuola Norm.Sup. Pisa, 35–68(1981)

    Google Scholar 

  17. Horrocks G. and Munford D., Topology. Pergman Press 12,63–81(1973).

    CrossRef  Google Scholar 

  18. Ionescu P., An enumeration of all smooth projective varieties of degree 5 and 6. I.N.C.R.E.S.T. Preprint Series Math. 74(1981).

    Google Scholar 

  19. Ionescu P., Embedded projective varieties of small invariants. Proc. of the week of Algebraic Geometry, Bucharest (1982). Lect. Notes Math. Vol. 1056 Berlin, Heidelberg, New York. Springer Verlag (1984).

    MATH  Google Scholar 

  20. Ionescu P., On varieties whose degree is small with respect to codimension. Math.Ann. 27, 339–348(1985).

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Lanteri A., Sulle superfici di grado sette. Ist.Lombardo (Rend.Sc.) A115,171–189(1981).

    MathSciNet  Google Scholar 

  22. Lanteri A. and Palleschi M., Sulle superfici di grado piccolo in P 4. Ist.Lombardo (Rend.Sc.) A113, 224–241(1979).

    MathSciNet  MATH  Google Scholar 

  23. Livorni E.L., Classification of algebraic surfaces with sectional genus less then or equal to six: Rational surfaces. Pac. J. Math. Vol.113, No.1, 93–114(1984).

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. Livorni E.L., Classification of algebraic non-ruled surfaces with sectional genus less than or equal to six. Nagoya J. Math. Vol.100, 1–9(1985).

    MathSciNet  MATH  Google Scholar 

  25. Livorni E.L., Classification of algebraic surfaces with sectional genus less than or equal to six. II Ruled surfaces with dim ΦKx⊗L (X)=1. Can.J.Math. Vol.XXXVII,No.4, 1110–1121(1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. Livorni E.L., Classification of algebraic surfaces with sectional genus less than or equal to six. II Ruled surfaces with dim ΦKx⊗L (X)=2. Math. Scand. 58,9–29(1986).

    MathSciNet  MATH  Google Scholar 

  27. Okonek C., Moduli reflexiver Garben und Flächen von kleinem Grad. in P 4. Math.Z. 184, 549–572(1983).

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. Okonek C., Über 2-codimensionale Untermannigfaltigkeiten vom Grad 7 in P 4 und P 5. Math.Z. 187, 209–219(1984).

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. Okonek C., Fächen vom Grad 8 in P 4. Math.Z. 191, 207–223(1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. Picard E. and Simart G., Théories des Fonctions Algebriques de Deux Variables Indépendantes, Chelsea Pub.Co., Bronx, New York (1971)

    MATH  Google Scholar 

  31. Reider I., Vector bundles of rank 2 and linear systems on algebraic surfaces. Ann.Math. 127,309–316(1988).

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. Room T.G., The Geometry of Determinantal loci. Cambridge University Press (1938)

    Google Scholar 

  33. Roth L., On surfaces of sectional genus four. Proc. Cambridge Phil.Soc.29, 184–194(1933).

    CrossRef  MATH  Google Scholar 

  34. Roth L., On surfaces of sectional genus five. Proc. Cambridge Phil.Soc.30, 123–133 (1934).

    CrossRef  MATH  Google Scholar 

  35. Roth L., On the regularity of surfaces I,II,III. Proc. Cambridge Phil.Soc.30, 4–14, 271–286, 404–408(1934).

    CrossRef  MATH  Google Scholar 

  36. Roth L., On surfaces of sectional genus six. Proc. Cambridge Phil.Soc.32, 355–365(1936).

    CrossRef  MATH  Google Scholar 

  37. Roth L., On the projective classification of surfaces. Proc. London Math. Soc.(2) 42, 142–170 (1937).

    CrossRef  MathSciNet  MATH  Google Scholar 

  38. Serrano F., The adjunction mapping and hyperelliptic divisors on a surface. Preprint.

    Google Scholar 

  39. Sommese A.J., Hyperplane sections of projective surfaces I. The adjunction mapping. Duke Math. J.,46, 377–401(1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  40. Sommese A.J. and Van de Ven A., On the adjunction mapping. Math.Ann.278,593–603(1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  41. Van de Ven A., On the 2-connectedness of very ample divisors on a surface. Duke Math.J. 46, 403–407(1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1990 Springer-Verlag

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Livorni, E.L. (1990). On the existence of some surfaces. In: Sommese, A.J., Biancofiore, A., Livorni, E.L. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 1417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083340

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  • DOI: https://doi.org/10.1007/BFb0083340

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