Maximal rank curves and singular points of the Hilbert scheme

Giorgio Bolondi; Jan O. Kleppe; Rosa Maria Miro-Roig

Compositio Mathematica (1991)

  • Volume: 77, Issue: 3, page 269-291
  • ISSN: 0010-437X

How to cite


Bolondi, Giorgio, Kleppe, Jan O., and Miro-Roig, Rosa Maria. "Maximal rank curves and singular points of the Hilbert scheme." Compositio Mathematica 77.3 (1991): 269-291. <>.

author = {Bolondi, Giorgio, Kleppe, Jan O., Miro-Roig, Rosa Maria},
journal = {Compositio Mathematica},
keywords = {linkage; Hilbert scheme; maximal rank; obstructed curves; liaison; natural cohomology},
language = {eng},
number = {3},
pages = {269-291},
publisher = {Kluwer Academic Publishers},
title = {Maximal rank curves and singular points of the Hilbert scheme},
url = {},
volume = {77},
year = {1991},

AU - Bolondi, Giorgio
AU - Kleppe, Jan O.
AU - Miro-Roig, Rosa Maria
TI - Maximal rank curves and singular points of the Hilbert scheme
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 77
IS - 3
SP - 269
EP - 291
LA - eng
KW - linkage; Hilbert scheme; maximal rank; obstructed curves; liaison; natural cohomology
UR -
ER -


  1. [B] G. Bolondi: Irreducible families of curves with fixed cohomology. Arch. der Math.53 (1989), 300-305 Zbl0658.14005MR1006724
  2. [BB] E. Ballico and G. Bolondi: Deficiency modules and specialization. To appear in Proc. A.M.S. Zbl0701.14028MR990412
  3. [BM] G. Bolondi and J.C. Migliore: Classification of maximal rank curves in the liaison class Ln, Math. Ann.277 (1987), 585-603. Zbl0607.14015MR901706
  4. [BS] D. Bayer and M. Stillman: Macaulay, version 3.0 (1989). 
  5. [C] M.C. Chang: Characterization of arithmetically Buchsbaum subschemes of codimension 2 in P''. Preprint (1987). Zbl0663.14034
  6. [E] Ph. Ellia: D'autres composantes non réduites de Hilb P3. Math. Ann.277 (1987), 433-446. Zbl0635.14006MR891584
  7. [EF] Ph. Ellia and M. Fiorentini: Défaut de postulation et singularités du Schéma de Hilbert. Annali Univ. di Ferrara30 (1984) 185-198. Zbl0577.14019MR796926
  8. [El] G. Ellinsgrud: Sur le schéma d'Hilbert des variétés de codimension 2 dans Pe à cône de Cohen-Macaulay. Ann. Sc. Ec. Norm. Sup.2 (1975), 423-432. Zbl0325.14002MR393020
  9. [K1] J.O. Kleppe: The Hilbert-flag scheme, its properties and its connection with the Hilbert scheme. Applications to curve in the 3-space, Thesis, Univ. of Oslo (1981). 
  10. [K2] J.O. Kleppe: Deformations of graded algebras, Math. Scand.45 (1979, 205-231. Zbl0436.14004MR580600
  11. [K3] J.O. Kleppe: Non-reduced components of the Hilbert scheme of smooth space curves, in Space Curves, Proceedings Rocca di Papa1985, Springer Lecture Notes in Math.1266. Springer1987. Zbl0631.14022MR908714
  12. [K4] J.O. Kleppe: Liaison of families of subschemes , in Pn, In: Algebraic Curves and Projective Geometry, Proceedings Trento1988, Springer Lecture Notes in Math.1389, 128-173. Springer, 1989. Zbl0697.14003MR1023396
  13. [M1] D. Mumford: Further pathologies in algebraic geometry, Amer. J. Math.89 (1962), 642-648. Zbl0114.13106MR148670
  14. [PS] Chr. Peskine and L. Szpiro: Liaison des variétés algébriques, Inv. Math.26 (1974), 271-302. Zbl0298.14022MR364271
  15. [PiS] R. Piene and D. Schlessinger: On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math.107 (1985), 761-774. Zbl0589.14009MR796901
  16. [S] E. Sernesi: Un esempio di curva ostruita in P3. Sem. di variabili Complesse, Bologna (1981), 223-231. MR770798
  17. [SGA2] A. Grothendieck: Cohomologie locale des faisceaux cohérents et Théorèmes de Lefschetz locaux et globaux, North-Holland, Amsterdam, 1968. Zbl0197.47202MR476737
  18. [W] Ch. Walter: Some examples of obstructed curves in P3. 

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.