论文标题
修剪络合物和应用于确定方面理想的分辨率
Trimming Complexes and Applications to Resolutions of Determinantal Facet Ideals
论文作者
论文摘要
我们生产一个称为修剪复合物并探索应用的复合体系列。我们研究如何使用修剪络合物来推导贝蒂表，以最小的自由分辨率，以最小化为任意理想$ i $的生成集生成集生成的理想。特别是，我们计算了Betti表，用于从宽带偏差的对称矩阵$ m $的次最大Pfaffians中删除任意发电机。我们还明确地计算了Betti表的理想，该理想是由通用$ n \ times m $矩阵的最大未成年人理想的某些子集生成的。这样的理想是称为确定方面理想的一类理想的子集，其更高程度的betti数字以前尚未计算出来。
We produce a family of complexes called trimming complexes and explore applications. We study how trimming complexes can be used to deduce the Betti table for the minimal free resolution of the ideal generated by subsets of a generating set for an arbitrary ideal $I$. In particular, we compute the Betti table for removing an arbitrary generator from the ideal of submaximal pfaffians of a generic skew symmetric matrix $M$. We also explicitly compute the Betti table for the ideal generated by certain subsets of the generating set of the ideal of maximal minors of a generic $n \times m$ matrix. Such ideals are a subset of a class of ideals called determinantal facet ideals, whose higher degree Betti numbers had not previously been computed.
