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

Abstract

We study H. Dao's invariant ${\eta }_c^R$ of pairs of modules defined over a complete intersection ring $R$ of codimension $c$ having an isolated singularity. Our main result is that ${\eta }_c^R$ 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.

14 pages. Appendix added

References in corpus (1)

• Asymptotic behavior of Tor over complete intersections and applications

Cited by in corpus (1)

• Torsion in tensor products, and tensor powers, of modules