Toric Ideals Generated by Quadratic Binomials
Toric Ideals Generated by Quadratic Binomials
复制标题
由二次二项式生成的环面理想
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
T. Hibi
中科院分区：
文献类型：
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作者：
Hidefumi Ohsugi;T. Hibi
摘要研究了由二次二项式生成的有限图所产生的环理想的组合判据。这个判据保证了由无平方二次多项式生成的每一个科祖尔代数都是正态的。给出了一个环理想由二次二项式生成的正规非Koszul无平方半群环的例子，以及一个环理想不具有二次Grobner基的非正规Koszul无平方半群环的例子。此外，对所有由无平方二次单项式生成的具有2线性分辨率的仿射半群环进行了分类。此外，还证明了由二次单项式生成的正仿射半群环的环面理想是由二次二项式生成的，如果其下多面体是简单的。
Abstract A combinatorial criterion for the toric ideal arising from a finite graph to be generated by quadratic binomials is studied. Such a criterion guarantees that every Koszul algebra generated by squarefree quadratic monomials is normal. We present an example of a normal non-Koszul squarefree semigroup ring whose toric ideal is generated by quadratic binomials as well as an example of a non-normal Koszul squarefree semigroup ring whose toric ideal possesses no quadratic Grobner basis. In addition, all the affine semigroup rings which are generated by squarefree quadratic monomials and which have 2-linear resolutions will be classified. Moreover, it is shown that the toric ideal of a normal affine semigroup ring generated by quadratic monomials is generated by quadratic binomials if its underlying polytope is simple.