Betti numbers of symmetric shifted ideals
Betti numbers of symmetric shifted ideals
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DOI：
10.1016/j.jalgebra.2020.04.037
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发表时间：
2019-07
影响因子：
0.9
通讯作者：
Jennifer Biermann;Hernán de Alba;Federico Galetto;S. Murai;U. Nagel;Augustine O’Keefe;Tim Römer;A. Seceleanu
中科院分区：
文献类型：
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作者：
Jennifer Biermann;Hernán de Alba;Federico Galetto;S. Murai;U. Nagel;Augustine O’Keefe;Tim Römer;A. Seceleanu
我们引入一类新的单项式理想，我们称之为对称移位理想。对称移位理想被对称群的自然作用所固定，并且在由该作用所固定的单项理想类中，它们可以被认为是单项理想类中稳定单项理想的类似物。我们证明了对称移位理想具有线性同分项，并计算了它的（等变）分次Betti数。作为这一结果的应用，我们得到了星星构型的定义理想的符号幂的分次Betti数的几个推论.
We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetric shifted ideal has linear quotients and compute its (equivariant) graded Betti numbers. As an application of this result, we obtain several consequences for graded Betti numbers of symbolic powers of defining ideals of star configurations.