manuscripta mathematica

, Volume 64, Issue 2, pp 205–211 | Cite as

Deformations of arithmetically Cohen-Macaulay subvarieties of pn

  • Giorgio Bolondi
  • Rosa Maria Mirò-Roig


We show that every arithmetically Cohen-Macaulay two-codimensional subscheme ofPn can be deformed to a reduced union of two-codimensional linear subvarieties. This problem (classical for curves with the name of Zeuthen problem) was solved for curves by F.Gaeta.


Number Theory Algebraic Geometry Topological Group Linear Subvariety 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B]
    BOLONDI,G.;Zeuthen problem and cohomology Preprint U.T.M.226, Trento (1987)Google Scholar
  2. [BM1]
    BOLONDI,G.; MIGLIORE,J.C.;The structure of an even liaison class. Preprint U.T.M.239, Trento (1988)Google Scholar
  3. [BM2]
    BOLONDI,G.;MIGLIORE,J.C.;Configurations of Linear Projective Subvarieties. To appear in: Proceedings of the Trento Conference on Algebraic Curves and Projective Geometry, 1988, Springer Lect. Notes in Math.Google Scholar
  4. [CGO]
    CILIBERTO,C; GERAMITA,A.V.; ORECCHIA,F.;Remarks on a theorem of Hilbert-Burch Queen's University Preprints, 23-1986Google Scholar
  5. [E]
    ELLINSGRUD,G.;Sur le schema de Hilbert des varietes de codimension 2 dans P e à cone de Cohen-Macaulay. Ann. Sc. Ec. Norm. Sup. t.8, fasc. 4(1975), 423–431Google Scholar
  6. [G]
    GAETA,F.;Nuove ricerche sulle curve sghembe algebriche di residuale finito e sui gruppi di punti del piano Ann. Mat. Pura e Appl.31 (1950), 1–64Google Scholar
  7. [GP]
    GRUSON,L.; PESKINE,Chr.;Genre des courbes de l'espace projectif (1) ln:“Algebraic geometry, Proceedings Tromsø, Norway (1977)”. Lect. Notes in Math.687. Berlin,Heidelberg,New York: Springer 1978Google Scholar
  8. [HH]
    HARTSHORNE,R.; HIRSCHOWITZ,A.;Smoothing algebraic space curves ln:“Algebraic Geometry, Sitges (Barcelona) 1983”. Lect. Notes in Math.1124, 98–131. Berlin, Heidelberg, New York: Springer 1985Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Giorgio Bolondi
    • 1
  • Rosa Maria Mirò-Roig
    • 2
  1. 1.Dipartimento di Matematica e FisicaUniversità di CamerinoCamerino (Macerata)Italy
  2. 2.Departament d'Algebra i Geometria Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations