عنوان	Componentwise linear powers and the $x$-condition
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	componentwise linear, $x$-condition, symmetric powers, vertex cover ideals
چکیده	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 Gr\"obner 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 $\R(I)$ of a graded ideal or the symmetric algebra $\Sym(M)$ 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.
پژوهشگران	یورگن هرزوگ (نفر اول)، تاکایوکی هیبی (نفر دوم)، سمیه مرادی (نفر سوم)