论文标题
零部性线性功率和$ x $ - 条件
Componentwise linear powers and the $x$-condition
论文作者
论文摘要
令$ s = k [x_1，\ ldots，x_n] $是字段上的多项式环，$ a $ a标准分级$ s $ algebra。就定义理想的$ j $ a $ a $的gröbner而言，我们提供的条件称为X条件，这意味着所有分级组件$ a_k $ a_k $ a $ a $具有线性的商，并且具有其他假设为componentswisewise linearear。这种代数的一个典型例子是分级理想的rees环$ r（i）$或模块$ m $的对称代数$ sym（m）$。我们应用我们的标准来研究某些对称代数，并且顶点的力量涵盖了某些类别图的理想。
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 $R(I)$ 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.
