## Regularity bounds for Koszul cycles

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- by Aldo Conca and Satoshi Murai PDF
- Proc. Amer. Math. Soc.
**143**(2015), 493-503 Request permission

## Abstract:

We study the Castelnuovo-Mumford regularity of 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 $M$ in the homological position $t\in {\mathbb {N}}$. Under mild assumptions on the base field we prove that $\operatorname {reg} Z_t(I,S)$ is a subadditive function of $t$ when $\operatorname {dim} S/I=0$. For Borel-fixed ideals $I,J$ we prove that $\operatorname {reg} Z_t(I,S/J)\leq t(1+ \operatorname {reg} I)+\operatorname {reg} S/J$, a result already announced by Bruns, Conca and Römer.## References

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## Additional Information

**Aldo Conca**- Affiliation: Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- MR Author ID: 335439
- Email: conca@dima.unige.it
**Satoshi Murai**- Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan
- MR Author ID: 800440
- Email: s-murai@ist.osaka-u.ac.jp
- Received by editor(s): October 11, 2012
- Received by editor(s) in revised form: May 2, 2013
- Published electronically: October 24, 2014
- Additional Notes: The research of the second author was partially supported by KAKENHI 22740018
- Communicated by: Irena Peeva
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**143**(2015), 493-503 - MSC (2010): Primary 13D02, 13D03
- DOI: https://doi.org/10.1090/S0002-9939-2014-12292-1
- MathSciNet review: 3283639