Combinatorial study of stable categories of graded Cohen–Macaulay modules over skew quadric hypersurfaces
Combinatorial study of stable categories of graded Cohen–Macaulay modules over skew quadric hypersurfaces
复制标题
DOI：
10.1007/s13348-020-00306-1
复制
发表时间：
2019-10
影响因子：
1.1
通讯作者：
A. Higashitani;Kenta Ueyama
中科院分区：
文献类型：
--
作者：
A. Higashitani;Kenta Ueyama
本文提出了非对易超曲面的表示理论与组合学之间的一种新的联系。设是1次和1次的分次()-斜多项式代数。我们证明了分次极大Cohen-Macaulay模环/(F)的稳定范畴可以用这四种图解运算完全计算出来。因此，等价于派生范畴，并且这是作为某一矩阵的零度得到的。利用Stanley-Reisner理想的性质，我们还证明了S的点格式同构于的不可约分支的个数小于或等于$$\Left({\Begin{阵列}{c}r+1\\2\end{阵列}}\右侧)$$。
In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. LetSbe a graded ()-skew polynomial algebra innvariables of degree 1 and. We prove that the stable categoryof graded maximal Cohen–Macaulay module overS/(f) can be completely computed using the four graphical operations. As a consequence,is equivalent to the derived category, and thisris obtained as the nullity of a certain matrix over. Using the properties of Stanley–Reisner ideals, we also show that the number of irreducible components of the point scheme ofSthat are isomorphic tois less than or equal to $$\left( {\begin{array}{c}r+1\\ 2\end{array}}\right) $$.