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Gorenstein Schemes on General Hypersurfaces of ℙr

Published online by Cambridge University Press:  22 January 2016

Alfio Ragusa  and
Giuseppe Zappalà
Alfio Ragusa
Affiliation:
Dipartimento di Matematica, Università di Catania, Viale A. Doria 6 95125 Catania, Italy, ragusa@dipmat.unict.it
Giuseppe Zappalà
Affiliation:
Dipartimento di Matematica, Università di Catania, Viale A. Doria 6 95125 Catania, Italy, zappalag@dipmat.unict.it
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Abstract

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It is completely known the characterization of all Hilbert functions and all graded Betti numbers for 3-codimensional arithmetically Gorenstein subschemes of ℙr (works of Stanley [St] and Diesel [Di]). In this paper we want to study how geometrical information on the hypersurfaces of minimal degree containing such schemes affect both their Hilbert functions and graded Betti numbers. We concentrate mainly on the case of general hypersurfaces and of irreducible hypersurfaces, for which we find strong restrictions for the Hilbert functions and graded Betti numbers of their subschemes.

Keywords

13D4013H10

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 162 , June 2001 , pp. 111 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

[BE] Buchsbaum, D. A. and Eisenbud, D., Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3, Amer. J. Math., 99 (1) (1977), 447–485.Google Scholar
[CV] Conca, A. and Valla, G., Betti numbers and lifting of Gorenstein codimension three ideals, preprint.Google Scholar
[DV] De Negri, E. and Valla, G., The h-vector of a Gorenstein codimension three domain, Nagoya Math. J., 13 (1995), 113–140.Google Scholar
[Di] Diesel, S., Irreducibility and dimension theorems for families of height 3 Goren-stein algebras, Pac. J. of Math., 172 (4) (1996), 365–397.CrossRefGoogle Scholar
[GM] Geramita, A. and Migliore, J., Reduced Gorenstein codimension three subschemes of projective space, Proc. Amer. Math. Soc., 125 (4) (1997), 943–950.Google Scholar
[Ha] Harima, T., Some examples of unimodal Gorenstein sequences, J. Pure Appl. Algebra, 103 (1995), 313–324.Google Scholar
[HTV] Herzog, J., Trung, N. V. and Valla, G., On hyperplane sections of reduced irreducible varieties of low codimension, J. Math. Kyoto Univ., 34 (1) (1994), 47–72.Google Scholar
[IK] Iarrobino, A. and Kanev, V., The length of a homogeneous form, determinantal loci of catalecticants and Gorenstein algebras, preprint.Google Scholar
[RZ] Ragusa, A. and Zappalà, G., Properties of 3-codimensional Gorenstein schemes, to appear Comm. in Alg.Google Scholar
[St] Stanley, R., Hilbert functions of graded algebras, Adv. in Math., 28 (1978), 57–83.Google Scholar
[Ul] Ulrich, B., Sums of linked ideals, Trans. Am. Math. Soc., 318 (1990), 1–42.Google Scholar