arXiv 1001.05852010-01math.ACmath.AG

过滤自由分解

Filtering free resolutions

David Eisenbud, Daniel Erman, Frank-Olaf Schreyer

备注：: We correct a mistake in the proof of Corollary 4.2 in the published version of this paper. The mistake involves an incorrect definition for when two degree sequences are "sufficiently separated". The new definition weakens Theorem 1.3 somewhat, but the examples survive. We thank Amin Nematbakhsh and to Gunnar Floystad for bringing this mistake to our attention. We also correct some minor typos
发表信息：: Compositio Math. 149 (2013) 754-772
DOI：: 10.1112/S0010437X12000760

摘要：

Eisenbud-Schreyer和Boij-Söderberg最近的一个结果证明了任何分次模的Betti图分解为纯图的正有理线性组合。这种数值分解何时对应于最小自由分解的实际过滤？我们的主要结果给出了一个充分条件。我们应用它证明了具有某些可解的Betti图的自由分解的不存在性，并研究了最简单的“野生”图的表示半群。

英文摘要：

A recent result of Eisenbud-Schreyer and Boij-Söderberg proves that the Betti diagram of any graded module decomposes as a positive rational linear combination of pure diagrams. When does this numerical decomposition correspond to an actual filtration of the minimal free resolution? Our main result gives a sufficient condition for this to happen. We apply it to show the non-existence of free resolutions with some plausible-looking Betti diagrams and to study the semigroup of quiver representations of the simplest "wild" quiver.

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