Koszul almost complete intersections
Koszul almost complete intersections
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DOI：
10.1016/j.jalgebra.2017.12.020
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发表时间：
2018-01
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影响因子：
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通讯作者：
Matthew Mastroeni
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文献类型：
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作者：
Matthew Mastroeni
设R= S/I是标准分次多项式环S与二次型生成的理想I的商。如果R是Koszul，Avramov，Conca和Iyengar的一个问题是问R在S上的Betti数是否可以在I的最小生成元数上由二项式系数上有界。受前人关于三个二次曲面定义的Koszul代数的结果的启发，我们对Koszul几乎完全交的结构进行了完整的分类，并在此过程中对所有此类环的上述问题给出了肯定的回答。
Abstract Let R= S/I be a quotient of a standard graded polynomial ring S by an ideal I generated by quadrics. If R is Koszul, a question of Avramov, Conca, and Iyengar asks whether the Betti numbers of R over S can be bounded above by binomial coefficients on the minimal number of generators of I. Motivated by previous results for Koszul algebras defined by three quadrics, we give a complete classification of the structure of Koszul almost complete intersections and, in the process, give an affirmative answer to the above question for all such rings.