Burch index, summands of syzygies and linearity in resolutions
Abstract
The Burch index is a new invariant of a local ring R whose positivity implies a kind of linearity in resolutions of R-modules. For example, if R has depth zero and Burch index at least 2, then any non-free 7th R-syzygy contains the residue field as a direct summand. We also compute the Burch index in various cases of interest.
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