Advertisement

Annali dell’Università’ di Ferrara

, Volume 33, Issue 1, pp 89–111 | Cite as

Quelques remarques sur les courbes arithmétiquement Buchsbaum de l’espace projectif

  • Philippe Ellia
  • Mario Fiorentini
Article
  • 18 Downloads

Résumé

On donne (cf. §2) un théorème d’annulation pour la cohomologie des courbes gauches arithmétiquement Buchsbaum (a.B). On développe ensuite quelques conséquences de ce théorème. Notamment on donne une description détaillée des courbes a.B sous-canoniques (resp. quasi-intersections complètes) et de leurs proprietés (cf. § 3, 4). D’autres conséquences osnt mentionnées au § 5. Par ex. Prop. 5.5 résount une conjecture de Migliore sur les courbes a.B de rang maximum.

Sommario

Si dà (vedi §2) un teorema di annullamento per la coomologia delle curve aritmeticamente di Buchsbaum (a.B). Si sviluppano di seguito alcune, conseguenze di questo teorema. Più precisamente si dà una descrizione dettagliata delle curve a.B sotto-canoniche (risp. quasi-complete intersezioni) e delle loro proprietà (cf. § 3, 4). Ulteriori conseguenze sono indicate nel § 5. Per esempio la Prop. 5.5 risolve una congettura di Migliore sopra le curve a.B. di rango massimo.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. [A]M. Amasaki,On the structure of arithmetically Buchsbaum curves in P k3, RIMS, Kyoto University (1983).Google Scholar
  2. [A2]M. Amasaki,Examples of nonsingular irreducible curves which give reducible singular points of red(H d,g), RIMS, Kyoto University, 1984.Google Scholar
  3. [Ap]R. Apery,Sur les courbes de première espèce de l’espace à trois dimensions, C. R. Acad. Sc. Paris,220 (1945), pp. 271–272.MATHMathSciNetGoogle Scholar
  4. [BE]E. Ballico—Ph. Ellia,The maximal rank conjecture for nonspecial curves in P 3, Inv. Math. (1985), pp. 541–555.Google Scholar
  5. [BE2]E. BAllico—Ph. Ellia,Some more examples of curves in P 3 with stable normal bundle, J. für reine u. angew. Math., pp. 87–93.Google Scholar
  6. [Ba]W. Barth,Some properties of stable rank-2 vector bundles on P n″, Math. Ann.,226 (1977), pp. 125–150.MATHCrossRefMathSciNetGoogle Scholar
  7. [BoMi]G. Bolondi—J. Migliore,Classification of maximal rank curves in the liaison class L n (à paraître Math. Ann.), preprint, 1987.Google Scholar
  8. [Bo]G. Bolondi,Liaison and maximal rank, Boll. U.M.I., 1987.Google Scholar
  9. [Bo2]G. Bolondi,Smoothing algebraic curves by curvilinear reflexives sheaves, preprint.Google Scholar
  10. [BSV]H. Bresinsky—P. Schenzel—W. Vogel,On liaison, arithmetical Buchsbaum curves and monomial curves in P 3, J. of Alg. (1984), pp. 283–301.Google Scholar
  11. [EHV]L. EinR. HartshorneR. Vogelaar,Restriction theorems for stable rank 3 vector bundles on P n, Math. Ann.,259 (1982), pp. 541–569.MATHCrossRefMathSciNetGoogle Scholar
  12. [E]Ph. Ellia,Exemples de courbes de P 3 à fibré normal semi-stable, stable, Math. Ann. (1983), pp. 389–396.Google Scholar
  13. [EF]Ph. Ellia—M. Fiorentini,Défaut de postulation et singularités du schéma de Hilbert, Ann. Mat. Univ. Ferrara (1984), pp. 185–198.Google Scholar
  14. [gE]G. Ellingsrund,Sur le schéma de Hilbert des variétés de codimension 2dans P e à cône de Cohen-Macaulay, Ann. Sci. Ecole Norm. Sup. (1975), pp. 423–432.Google Scholar
  15. [FL]M. Fiorentini—A. T. Lascu,Two theorems of G. Gherardelli, Lect. Notes, 1056, Alg. Geometry, Bucharest (1982), pp. 132–141.Google Scholar
  16. [G]F. Gaeta,Sulle curve algebriche sghembe di residuale finito, Ann. di Mat. (1948), pp. 177–241.Google Scholar
  17. [G2]F. Gaeta,Quelques progrés récents dans la classification des variétés algébriques d’un espace projectif, «Deuxième Colloque de Géométrie Algébrique», Liège (1952), pp. 145–183.Google Scholar
  18. [GMV]A. V. GeratimaP. MarosciaW. Vogel,A note on arithmetically Buchsbaum curves in P 3, Dept. of Math. and Statistics, Queen’s University, Kingston, 1983, preprint.Google Scholar
  19. [Gh]G. Gherardelli,Sulle curve sghembe algebriche intersezioni complete di due superficie, Atti R. Acc. d’Italia (1943), pp. 128–132.Google Scholar
  20. [Gh2]G. Gherardelli,Sulle curve sghembe algebriche intersezioni semplici complete di tre superficie, Atti R. Acc. d’Italia (1943), pp. 460–462.Google Scholar
  21. [gF]F. Ghione,Anelli graduati di Cohen-Macaulay e funzione di Hilbert, Annali Mat. Università Ferrara,19 (1975), pp. 87–96.MathSciNetGoogle Scholar
  22. [GM]H. Grauert—G. Mülich,Vektorbündel vom rank 2 über dem n-dimensionalen komplex projective Raum, Man. Math. (1975), pp. 75–100.Google Scholar
  23. [GP]L. Gruson—C. Peskine,Genere des courbes de l’espace projectif, Lecture Notes, 687 (1977).Google Scholar
  24. [GP2]L. GrusonC. Peskine,Postulation des courbes gauches, Lect. Notes in Mathematics, 997 (1983), pp. 218–227.MathSciNetGoogle Scholar
  25. [Ha]R. Hartshorne,Stable vector bundles of rank 2 on P 3, Math. Ann. (1978), pp. 229–280.Google Scholar
  26. [Ha2]R. Hartshorne,Stable reflexive sheaves, Math. Ann. (1980), pp. 121–176.Google Scholar
  27. [HH]R. HartshorneA. Hirschowitz,Smoothing algebraic space curves, Lect. Notes in Math., n. 1124 (1983), pp. 98–131.MathSciNetCrossRefGoogle Scholar
  28. [K]J. O. Kleppe,The Hilbert-flag scheme, its properties and its connection with the Hilbert scheme, Inst. of Math. Univ. Oslo, 1981.Google Scholar
  29. [M]D. Mumford,Lectures on curves on an algebraic surface, Princeton Univ. Press, 1966.Google Scholar
  30. [Mi]G. Migliore,Buchsbaum curves in P 3, Preprint, 1987.Google Scholar
  31. [OSS]C. Okonek—M. Schneider—H. Spindler,Vector bundles on complex projective spaces, Progress in Mathematics, Birkhauser, 1980.Google Scholar
  32. [P]D. Perrin,Courbes passant par k points généraux de P 3, C. R. Acad. Sc. Paris (1984), pp. 451–453.Google Scholar
  33. [PS]C. Peskine—L. Szpiro,Liaison des variétés algébriques, Inv. Math. (1974), pp. 271–302.Google Scholar
  34. [R]P. Rao,Liaison among curves in P 3, Inv. Math. (1979), pp. 205–217.Google Scholar
  35. [Sc]P. Schwartau,Liaison Addition and Monomial Ideals, Ph. D. thesis, Brandeis University, 1982.Google Scholar
  36. [S]J. P. Serre,Sur les modules projectifs, Séminaire Dubreil, 1960/61.Google Scholar
  37. [SV]J. Stuckrad—W. Vogel,Toward a theory of Buchsbaum singularities, Amer. J. Math. (1978), pp. 727–746.Google Scholar
  38. [SW]P. Schenzel—W. Vogel,On liaison and arithmetical Buchsbaum curves in P 3, Astérisque (1981).Google Scholar

Copyright information

© Università degli Studi di Ferrara 1987

Authors and Affiliations

  • Philippe Ellia
    • 1
  • Mario Fiorentini
    • 2
  1. 1.CNRS UA 168, Dép. de MathématiquesUniversité de NiceNice(France)
  2. 2.Dipartimento di MatematicaUniversità di FerraraFerrara(Italia)

Personalised recommendations