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arXiv · 1110.2442

The vanishing of a higher codimension analog of Hochster's theta invariant

W. Frank Moore·Greg Piepmeyer·Sandra Spiroff·Mark E. Walker
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Abstract

We study H. Dao's invariant $η_c^R$ of pairs of modules defined over a complete intersection ring $R$ of codimension $c$ having an isolated singularity. Our main result is that $η_c^R$ vanishes for all pairs of modules when $R$ is a {\em graded} complete intersection ring of codimension $c > 1$ having an isolated singularity. A consequence of this result is that all pairs of modules over such a ring are $c$-$\Tor$-rigid.

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W. Frank Moore, Greg Piepmeyer, Sandra Spiroff, Mark E. Walker. 2012-05-22. The vanishing of a higher codimension analog of Hochster's theta invariant. https://arxiv.org/abs/1110.2442

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