Regularity bounds for Koszul cycles

Details Regularity bounds for Koszul cycles Regularity bounds for Koszul cycles

2012-03-08

arxiv.org/abs/1203.1783v1

Mathematics

Commutative Algebra

Scientific paper

We study the module of Koszul cycles $Z_t(I,M)$ of a homogeneous ideal $I$ in a polynomial ring $S$ with respect to a graded module $M$. Under mild assumptions on the base field we prove that the regularity of $Z_t(I,S)$ is a subadditive function of the homological position t when I is 0-dimensional. For Borel-fixed ideals $I$ and $J$ we prove that the regularity of $Z_t(I,S/J)$ is bounded above by $t(1+\reg I)+\reg S/J$.

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