Pacific Journal of Mathematics

On the postulation of $0$-dimensional subschemes on a smooth quadric.

S. Giuffrida, R. Maggioni, and A. Ragusa

Article information

Pacific J. Math., Volume 155, Number 2 (1992), 251-282.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35}
Secondary: 14M07: Low codimension problems


Giuffrida, S.; Maggioni, R.; Ragusa, A. On the postulation of $0$-dimensional subschemes on a smooth quadric. Pacific J. Math. 155 (1992), no. 2, 251--282.

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  • [AF] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules,GTM
  • [13] Springer-Verlag, New York, 1973.
  • [B] E. Ballico, Generatorsfor the homogeneous ideal of s general points in P3, J. Algebra, 106 (1987),46-52.
  • [BG] E. Ballico and A. V. Geramita, The minimal free resolution of the ideal of s general points in P 3 , Canad. Math. Soc. Conf. Proc, 6 (1986), 1-10.
  • [CGO] C. Ciliberto, A. V. Geramita, and F.Orecchia, Perfect varieties with defining equations of high degree,Boll. Un.Mat. Ital. 7, 1-B, (1987),633-647.
  • [D] E. Davis, ^-dimensionalsubschemes of P 2 : new application of Castelnuovo function, Ann. Univ. Ferrara, sez. VII, Sc. Mat.,32 (1986),93-107.
  • [DGO] E. Davis, A. V. Geramita, and F. Orecchia, Gorenstein algebras and the Cayley-Bacharach theorem, Proc. Amer. Math. Soc, 93 (1985),593-597.
  • [E] G. Ellingsrud,Sur le schema de Hilbert des varietes de codimension 2 dans Pe a cone de Cohen-Macaulay, Ann. Sc. Ec.Norm. Sup.,t. 8 fasc. 4 (1975), 423-431.
  • [GM] A. V. Geramita and P. Maroscia, The ideal offorms vanishing at a finite set of points in Pw , J. Algebra, 90 (1984),528-555.
  • [GMR] A. V. Geramita, P. Maroscia, and L. Roberts, The Hilbert function of a reduced k-algebra,J. London Math. Soc, (2),28 (1983),443-452.
  • [G] S. Giuffrida, Hilbertfunction of a 0-cycle in P 2 , Le Matematiche, Vol. XV, Fasc I-II (1985),252-266.
  • [GMa] S. Giuffrida and R. Maggioni, On the Rao module of a curve lying on a smooth cubic surface in P 3 , Comm. in Algebra, 18 (7), (1990), 2039-2061.
  • [GP1] L. Gruson and C. Peskine, Genredes courbes de espaceprojectif,Algebraic Geometry, Lecture Notes in Math. no. 687, Springer, 1978.
  • [GP2] L. Gruson and C. Peskine, Section plane d'une courbe gauche: postulation, Prog, in Math., 24 Birkhauser(1982), 33-35.
  • [Hb] B. Harbourne, The geometry of rational surfaces and Hilbert functions of points in the plane, Canad. Math. Soc, Conf. Proc, 6 (1986),95-111.
  • [HE] J. Harris and D. Eisenbud,Curves in projective space, Math. Super. Universite de Montreal, 1982.
  • [H] R. Hartshorne, AlgebraicGeometry, GTM 52, Springer-Verlag,Berlin, 1977.
  • [MR1] R. MaggioniandA. Ragusa, Connections between Hubert function and geo- metric properties for a finite set of points in P 2 , Le Matematiche, Vol. XXXIX, Fasc. I-II (1984), 153-170.
  • [MR2] R. MaggioniandA. Ragusa, TheHilbert function of generic plane sections of curves in P 3 , Inv. Math., 91 (1988),253-258.
  • [M] P.Maroscia, Some problems and results onfinitesets ofpoints in P 2 ,Lecture Notes in Math. no. 977,Springer-Verlag (1982),290-314.
  • [MV] P. Maroscia andW. Vogel, On the defining equations of points in general position in Pn , Math. Ann., 269(1984), 183-189.
  • [PS] C.Peskine andL. Szpiro, Liaison des varietes algbriques I,Invent. Math., 26 (1974),271-302.
  • [R1] G.Raditi, Hilbertfunction andgeometric propertiesfor a closed zero-dimen- sional subscheme of a quadric c P 3 ,to appear on Comm. in Algebra.
  • [R2] G.Raditi, Constructionof a set of pointson a smoothquadric c P3with assigned Hilbert function, Queen's Papers in Pure andApplied Math., 83 (1989), art. J.
  • [Sa] T.Sauer,Thenumber of equations definingpoints ingeneral position, Pacific J. Math., 120 (1985),199-213.
  • [St] R. Stanley, Hilbert function of graded algebras, Adv. in Math., 28(1978), 57-83.
  • [S] R.Strano, Sullesezioni iperpiane delle curve,Rend. Sem.Mat.eFis.Milano, 57(1987), 125-134.