In this paper we prove the existence of minimal level artinian graded algebras having socle degree r and type t and describe their h-vector in terms of the r-binomial expansion of t. We also investigate the graded Betti numbers of such algebras and completely describe their extremal resolutions. We also show that any set of points in PP^n whose Hilbert function has first difference as described above, must satisfy the Cayley-Bacharach property.

Level Algebras, Lex Segments and Minimal Hilbert Functions

BIGATTI, ANNA MARIA;GERAMITA, ANTHONY VITO
2003

Abstract

In this paper we prove the existence of minimal level artinian graded algebras having socle degree r and type t and describe their h-vector in terms of the r-binomial expansion of t. We also investigate the graded Betti numbers of such algebras and completely describe their extremal resolutions. We also show that any set of points in PP^n whose Hilbert function has first difference as described above, must satisfy the Cayley-Bacharach property.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/208987
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