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The vanishing of a higher codimension analog of Hochster's theta invariant (1110.2442v2)
Published 11 Oct 2011 in math.AC and math.AG
Abstract: We study H. Dao's invariant $\eta_cR$ of pairs of modules defined over a complete intersection ring $R$ of codimension $c$ having an isolated singularity. Our main result is that $\eta_cR$ 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.