%0 Journal Article %T Koszul cycles %A Winfreid Bruns %A Aldo Conca %A Tim R£żmer %J Mathematics %D 2010 %I arXiv %X 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. %U http://arxiv.org/abs/1009.1230v1