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.