论文标题
Burch索引，Syzygies的总和和线性的分辨率
Burch index, summands of syzygies and linearity in resolutions
论文作者
论文摘要
Burch索引是本地环$ r $的新不变性，其积极性意味着$ r $ $模型的分辨率有点线性。例如，如果$ r $具有零深度和伯奇指数至少$ 2 $，则任何非免费的7th $ r $ r $ syzygy都包含残留字段作为直接汇总。我们还计算了各种感兴趣的情况下的Burch指数。
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.
