论文标题
某些均衡单元理想的最小免费分辨率
Minimal Free Resolutions of Certain Equigenerated Monomial Ideals
论文作者
论文摘要
令$ r = k [x_1，\ dotsc，x_n] $表示字段$ k $上的标准分级多项式环。我们研究了某些类似的年度单体理想，其特性是所谓的互补理想在发电机上没有线性关系。然后，我们使用迭代的修剪复合物来推断出这种理想的贝蒂数字。此外，使用Miller和Rahmati的拆分映射锥的结果，我们为明确考虑的所有理想构建了最小的免费分辨率，并以有关这些复合物上的额外结构的问题得出结论。
Let $R = k[x_1, \dotsc , x_n]$ denote the standard graded polynomial ring over a field $k$. We study certain classes of equigenerated monomial ideals with the property that the so-called complementary ideal has no linear relations on the generators. We then use iterated trimming complexes to deduce Betti numbers for such ideals. Furthermore, using a result on splitting mapping cones by Miller and Rahmati, we construct the minimal free resolutions for all ideals under consideration explicitly and conclude with questions about extra structure on these complexes.
