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arXiv · 2208.05427

Burch index, summands of syzygies and linearity in resolutions

Hailong Dao·David Eisenbud
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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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Hailong Dao, David Eisenbud. 2022-08-10. Burch index, summands of syzygies and linearity in resolutions. https://arxiv.org/abs/2208.05427

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