Koszul homology and syzygies of Veronese subalgebras
Koszul homology and syzygies of Veronese subalgebras
复制标题
维罗内子代数的 Koszul 同源性和 syzygies
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Tim Römer
中科院分区：
文献类型：
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作者：
W. Bruns;A. Conca;Tim Römer
如果一个分级k代数R在1次上生成，在2次上有关系，并且在关系上的阶≤p的合集是线性的，则它具有Np的性质。R的Green-Lazarsfeld指标是满足性质Np的最大p。我们的主要结果表明（在基场的温和假设下）多项式环的第c次Veronese子带具有Green-Lazarsfeld指数≥c + 1。同样的结论也适用于任意标准的分级代数，提供$${cgg 0}$$。
A graded K-algebra R has property Np if it is generated in degree 1, has relations in degree 2 and the syzygies of order ≤ p on the relations are linear. The Green–Lazarsfeld index of R is the largest p such that it satisfies the property Np. Our main results assert that (under a mild assumption on the base field) the cth Veronese subring of a polynomial ring has Green–Lazarsfeld index ≥ c + 1. The same conclusion also holds for an arbitrary standard graded algebra, provided $${cgg 0}$$.