Nice Initial Complexes of Some Classical Ideals
Nice Initial Complexes of Some Classical Ideals
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DOI：
10.1090/conm/423/08073
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发表时间：
2005-12
期刊：
影响因子：
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通讯作者：
A. Conca;Serkan Hosten;Rekha R. Thomas
中科院分区：
文献类型：
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作者：
A. Conca;Serkan Hosten;Rekha R. Thomas
本文是关于交换代数和代数几何中被广泛研究的理想的Gorenstein初始复形的综述文章。其中包括Segre簇和Veronese簇的定义理想，称为Hibi理想的旗簇的环形变形，不定类矩阵的行列式理想，以及类斜对称矩阵的Pfaffian生成的理想。我们总结了最近关于构造无平方Gorenstein初始理想的工作，当这些理想本身是Gorenstein时。我们还给出了我们自己对Segre、Veronese和一些行列式情形的独立结果。
This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Veronese varieties, toric deformations of flag varieties known as Hibi ideals, determinantal ideals of generic matrices of indeterminates, and ideals generated by Pfaffians of generic skew symmetric matrices. We give a summary of recent work on the construction of squarefree Gorenstein initial ideals of these ideals when the ideals are themselves Gorenstein. We also present our own independent results for the Segre, Veronese, and some determinantal cases.