Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Intersection Multiplicities Over Gorenstein Rings, Claudia M. Miller, Anurag K. Singh
Intersection Multiplicities Over Gorenstein Rings, Claudia M. Miller, Anurag K. Singh
Mathematics - All Scholarship
We construct a complex of free-modules over a Gorenstein ring R of dimension five, for which the Euler characteristic and Dutta multiplicity are different. This complex is the resolution of an R-module of finite length and finite projective dimension. As a consequence, the ring R has a nonzero Todd class tau_3(R) and a bounded free complex whose local Chern character does not vanish on this class.
In the course of our work, we construct a module N of finite length and finite projective dimension over the hypersurface A=K[u,v,w,x,y,z]/(ux+vy+wz), such that the Serre intersection multiplicity of the modules N and A/(u,v,w)A …
Local Rings Of Countable Cohen-Macaulay Type, Craig Huneke, Graham J. Leuschke
Local Rings Of Countable Cohen-Macaulay Type, Craig Huneke, Graham J. Leuschke
Mathematics - All Scholarship
We prove (the excellent case of) Schreyer's conjecture that a local ring with countable Cohen-Macaulay type has at most a one-dimensional singular locus. Furthermore we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.