Koszul Cycles
نویسندگان
چکیده
We prove regularity bounds for Koszul cycles holding for every ideal of dimension ≤ 1 in a polynomial ring; see Theorem 3.5. In Theorem 4.7 we generalize the “c + 1” lower bound for the Green–Lazarsfeld index of Veronese rings proved in (Bruns et al., arXiv:0902.2431) to the multihomogeneous setting. For the Koszul complex of the c-th power of the maximal ideal in a Koszul ring we prove that the cycles of homological degree t and internal degree ≥ t(c + 1) belong to the t-th power of the module of 1-cycles; see Theorem 5.2.
منابع مشابه
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A standard associative graded algebra R over a field k is called Koszul if k admits a linear resolution as an R-module. A (right) R-module M is called Koszul if it admits a linear resolution too. Here we study a special class of Koszul algebras — roughly say, algebras having a lot of Koszul cyclic modules. Commutative algebras with similar properties (so-called algebras with Koszul filtrations)...
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