Burch index, summands of syzygies and linearity in resolutions
arXiv:2208.05427
Abstract
The Burch index is a new invariant of a local ring whose positivity implies a kind of linearity in resolutions of -modules. For example, if has depth zero and Burch index at least , then any non-free 7th -syzygy contains the residue field as a direct summand. We also compute the Burch index in various cases of interest.