Koszul cycles
Winfreid Bruns, Aldo Conca, Tim R\"omer
TL;DR
This paper establishes bounds on the regularity of Koszul cycles for low-dimensional ideals and extends previous results on the Green-Lazarsfeld index of Veronese rings to a multihomogeneous context.
Contribution
It provides new regularity bounds for Koszul cycles of certain ideals and generalizes the Green-Lazarsfeld index lower bound to multihomogeneous rings.
Findings
Proved regularity bounds for Koszul cycles of ideals with dimension ≤ 1.
Generalized Green-Lazarsfeld index lower bound to multihomogeneous Veronese rings.
Abstract
We prove regularity bounds for Koszul cycles holding for every ideal of dimension at most 1 in a polynomial ring. We generalize the lower bound for the Green-Lazarsfeld index of Veronese rings we proved in arXiv:0902.2431 to the multihomogeneous setting.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Graph theory and applications