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

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

2011-10-11

arxiv.org/abs/1110.2442v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

We study an invariant $\theta_c$ of pairs of modules defined over a complete intersection ring $R$ of codimension $c$ having an isolated singularity. (This invariant agrees, up to a constant factor, with H. Dao's invariant $\eta_c^R$.) Our main result is that $\theta_c^R$ 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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