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. The multiplicity and (Castelnuovo–Mumford) regularity of the symmetric algebra Sym(Syz_1(m)) are estimated by using the theory of s-sequences. It is proved that the multiplicity of Sym(Syz_1(m)) is 1 when n ≥ 5, and n − 2 is an upper bound for its regularity. In virtue of Gröbner bases, this bound is shown to be reached provided n ≤ 5.
On invariants of certain symmetric algebras
Restuccia, GaetanaMembro del Collaboration Group
;Tang, Zhongming
Membro del Collaboration Group
;Utano, RosannaMembro del Collaboration Group
2018-01-01
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. The multiplicity and (Castelnuovo–Mumford) regularity of the symmetric algebra Sym(Syz_1(m)) are estimated by using the theory of s-sequences. It is proved that the multiplicity of Sym(Syz_1(m)) is 1 when n ≥ 5, and n − 2 is an upper bound for its regularity. In virtue of Gröbner bases, this bound is shown to be reached provided n ≤ 5.File in questo prodotto:
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