分次模的广义矩阵Massey积
Generalized Matric Massey Products for Graded Modules
摘要：
广义矩阵Massey积理论在$A$ -模$M$上已经应用了一段时间，$A$是一个$k$ -代数.主要应用是计算局部形式模$\hat{H}_M$，同构于局部环的模的$A$ -模。这个理论也被推广到$\mathcal{O}_X$ -模$\mathcal{M}$，$X$是一个$k$ -概型.在这些注记中，我们考虑了广义Massey积的定义和任意阻塞情形下的关系代数（具有某些性质的微分分次$k$ -代数），并证明了这一理论适用于分次$R$ -模的情形，$R$是分次$k$ -代数，$k$是代数闭的.当关系代数是代数可化的，即关系是多项式而不是幂级数时，这给出了计算分次$R$ -模的开子集的组合方法.这也给出了$\mathcal{O}_{\Proj(R)}$ -模的模中的对应点为奇异的一个充分条件。计算是直接的，算法，并给出了一个例子的假设希尔伯特计划。
英文摘要：
The theory of generalized matric Massey products has been applied for some time to $A$-modules $M$, $A$ a $k$-algebra. The main application is to compute the local formal moduli $\hat{H}_M$, isomorphic to the local ring of the moduli of $A$-modules. This theory is also generalized to $\mathcal{O}_X$-modules $\mathcal{M}$, $X$ a $k$- scheme. In these notes we consider the definition of generalized Massey products and the relation algebra in any obstruction situation (a differential graded $k$-algebra with certain properties), and prove that this theory applies to the case of graded $R$-modules, $R$ a graded $k$-algebra, $k$ algebraically closed. When the relation algebra is algebraizable, that is the relations are polynomials rather than power series, this gives a combinatorial way to compute open (étale) subsets of the moduli of graded $R$-modules. This also gives a sufficient condition for the corresponding point in the moduli of $\mathcal{O}_{\Proj(R)}$-modules to be singular. The computations are straight forward, algorithmic, and an example on the postulation Hilbert scheme is given.
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