Hochster's theta invariant and the Hodge-Riemann bilinear relations

Details Hochster's theta invariant and the Hodge-Riemann bilinear relations Hochster's theta invariant and the Hodge-Riemann bilinear relations

2009-10-07

arxiv.org/abs/0910.1289v2

Mathematics

Commutative Algebra

20 pages

Scientific paper

Let R be an isolated hypersurface singularity, and let M and N be finitely generated R-modules. As R is a hypersurface, the torsion modules of M against N are eventually periodic of period two (i.e., Tor_i^R(M,N) is isomorphic to Tor_{i+2}^R(M,N) for i sufficiently large). Since R has only an isolated singularity, these torsion modules are of finite length for i sufficiently large. The theta invariant of the pair (M,N) is defined by Hochster to be length(Tor_{2i}^R(M,N)) - length(Tor_{2i+1}^R(M,N)) for i sufficiently large. H. Dao has conjectured that the theta invariant is zero for all pairs (M,N) when R has even dimension and contains a field. This paper proves this conjecture under the additional assumption that R is graded with its irrelevant maximal ideal giving the isolated singularity. We also give a careful analysis of the theta pairing when the dimension of R is odd, and relate it to a classical pairing on the smooth variety Proj(R).

Affiliated with

Also associated with

No associations

Rating

Hochster's theta invariant and the Hodge-Riemann bilinear relations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hochster's theta invariant and the Hodge-Riemann bilinear relations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hochster's theta invariant and the Hodge-Riemann bilinear relations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-36596