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- W2799299593 abstract "Let $${mathrm{Syz}}_1(mathfrak {m})$$ be the first syzygy of the graded maximal ideal $$mathfrak {m}$$ of a polynomial ring $$K[x_1,ldots ,x_n]$$ over a field K. The multiplicity and (Castelnuovo–Mumford) regularity of the symmetric algebra $${mathrm{Sym}}({mathrm{Syz}}_1(mathfrak {m}))$$ are estimated by using the theory of s-sequences. It is proved that the multiplicity of $${mathrm{Sym}}({mathrm{Syz}}_1(mathfrak {m}))$$ is 1 when $$nge 5$$ , and $$n-2$$ is an upper bound for its regularity. In virtue of Grobner bases, this bound is shown to be reached provided $$nle 5$$ ." @default.
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- W2799299593 date "2018-05-11" @default.
- W2799299593 modified "2023-10-18" @default.
- W2799299593 title "On invariants of certain symmetric algebras" @default.
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- W2799299593 doi "https://doi.org/10.1007/s10231-018-0756-6" @default.
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