9 research outputs found
Variation of Hilbert Coefficients
For a Noetherian local ring (\RR, \m), the first two Hilbert coefficients,
and , of the -adic filtration of an \m-primary ideal are
known to code for properties of \RR, of the blowup of \spec(\RR) along
, and even of their normalizations. We give estimations for these
coefficients when is enlarged (in the case of in the same integral
closure class) for general Noetherian local rings
Betti numbers for numerical semigroup rings
We survey results related to the magnitude of the Betti numbers of numerical
semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra
and Applications (V. Ene, E. Miller Eds.
Complete Intersection Dimension
A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained for modules of finite CI-dimension, providing the first class of modules of (possibly) infinite projective dimension with a rich structure theory of free resolutions