Let Syz_1(m) be the first syzygy of the graded maximal ideal m of a polynomial ring K[x_1,..., x_n] over a field K. Using the theory of s-sequences, the dimension and depth of the symmetric algebra Sym(Syz_1(m)) are calculated. As a conclusion, Sym(Syz_1(m)) is not Cohen–Macaulay for any n ≥ 4.
On the Symmetric Algebra of the First Syzygy of a Graded Maximal Ideal
RESTUCCIA, GaetanaMembro del Collaboration Group
;UTANO, RosannaMembro del Collaboration Group
2016-01-01
Abstract
Let Syz_1(m) be the first syzygy of the graded maximal ideal m of a polynomial ring K[x_1,..., x_n] over a field K. Using the theory of s-sequences, the dimension and depth of the symmetric algebra Sym(Syz_1(m)) are calculated. As a conclusion, Sym(Syz_1(m)) is not Cohen–Macaulay for any n ≥ 4.File in questo prodotto:
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