Level Algebras,Lex Segments,and Minimal Hilbert Functions |
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Abstract: | 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 ? n whose Hilbert function has first difference as described above, must satisfy the Cayley-Bacharach property. |
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Keywords: | Level algebras Lex segment Hilbert Functions Resolutions Points Cayley-Bacharach property |
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