Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case
Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case
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非Cohen-Macaulay情况下分级模块的Betti数和多重性猜想
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Jonas Soderberg
中科院分区：
文献类型：
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作者：
M. Boij;Jonas Soderberg
我们利用Eisenbud和Schreyer的结果证明了在标准的梯度多项式环上，任意一个梯度模的Betti图都是具有纯分辨率的模的Betti图的正线性组合。这意味着Herzog， Huneke和Srinivasan对不一定是Cohen-Macaulay的模块的多重性猜想。给出了纯图张成的简单扇形的凸性的一个组合证明。
We use the results by Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination Betti diagrams of modules with a pure resolution. This implies the Multiplicity Conjecture of Herzog, Huneke and Srinivasan for modules that are not necessarily Cohen-Macaulay. We give a combinatorial proof of the convexity of the simplicial fan spanned by the pure diagrams.