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• W3094031751 abstract "Let $S=K[x_1,ldots,x_n]$ be the polynomial ring over a field and $A$ a standard graded $S$-algebra. In terms of the Gröbner basis of the defining ideal $J$ of $A$ we give a condition, called the $x$-condition, which implies that all graded components $A_k$ of $A$ have linear quotients and with additional assumptions are componentwise linear. A typical example of such an algebra is the Rees ring $mathcal{R}(I)$ of a graded ideal or the symmetric algebra $textrm{Sym}(M)$ of a module $M$. We apply our criterion to study certain symmetric algebras and the powers of vertex cover ideals of certain classes of graphs." @default.
• W3094031751 created "2020-10-29" @default.
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• W3094031751 date "2022-12-04" @default.
• W3094031751 modified "2023-09-27" @default.
• W3094031751 title "Componentwise linear powers and the $x$-condition" @default.
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• W3094031751 doi "https://doi.org/10.7146/math.scand.a-133265" @default.
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