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

2011/10/11 by W. Frank Moore, Moore, W. Frank, Greg Piepmeyer +5
Mathematics · #13D02 #13D07 #14F20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13D02 #msc:13D07 #msc:14F20

paper · pdf · doi:10.48550/arxiv.1110.2442

14 pages. Appendix added

arxiv created 2012/05/22 · arxiv updated 2012/05/23

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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