Hilbert functions of irreducible arithmetically Gorenstein schemes

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.

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Hilbert functions and applications to the estimation of subspace arrangements

Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 ◽

10.1109/iccv.2005.114 ◽

2005 ◽

Cited By ~ 3

Author(s):

A.Y. Yang ◽

S. Rao ◽

A. Wagner ◽

Yi Ma ◽

R.M. Fossum

Keyword(s):

Hilbert Functions ◽

Subspace Arrangements

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FINITENESS OF HILBERT FUNCTIONS FOR GENERALIZED COHEN–MACAULAY MODULES

Communications in Algebra ◽

10.1081/agb-100001545 ◽

2001 ◽

Vol 29 (2) ◽

pp. 805-813 ◽

Cited By ~ 9

Author(s):

Vijaylaxmi Trivedi

Keyword(s):

Hilbert Functions

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Hilbert functions of monomial ideals containing a regular sequence

Israel Journal of Mathematics ◽

10.1007/s11856-016-1364-z ◽

2016 ◽

Vol 214 (2) ◽

pp. 857-865

Author(s):

Abed Abedelfatah

Keyword(s):

Regular Sequence ◽

Monomial Ideals ◽

Hilbert Functions

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Hilbert functions of colored quotient rings and a generalization of the Clements–Lindström theorem

Journal of Algebraic Combinatorics ◽

10.1007/s10801-014-0571-0 ◽

2014 ◽

Vol 42 (1) ◽

pp. 1-23

Author(s):

Kai Fong Ernest Chong

Keyword(s):

Hilbert Functions ◽

Quotient Rings ◽

Lindström Theorem

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Hilbert functions and the extension functor

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410007780x ◽

1989 ◽

Vol 105 (3) ◽

pp. 441-446 ◽

Cited By ~ 3

Author(s):

David Kirby

Keyword(s):

Commutative Ring ◽

Hilbert Functions ◽

Definition Of

Throughout R will denote a commutative ring with identity, A,B etc. will denote ideals of R, and E will denote a unitary R-module. We recall from [5] the definition of homological grade hgrR(A;E) as inf{r|ExtRr(R/A,E) ≠ 0}, and we allow both hgrR(A;E) = ∞ (i.e. ExtRr(R/A,E) = 0 for all r) and AE = E. For the most part E will be Noetherian, in which case hgrR(A;E) coincides with the usual grade grR(A;E) which is the supremum of the lengths of the (weak) E-sequences contained in A (see [7], for example).

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