Chennai Mathematical Institute


3:30pm-4:30pm, Lecture Hall 802
Local cohomology of Rees algebras and vanishing of normal Hilbert coefficients

J.K. Verma
Indian Institute of Technology, Bombay.


Normal Hilbert polynomials were introduced by David Rees. Rees characterised pseudo-rational local rings in terms of the vanishing of the constant term of the Normal Hilbert coefficient of all m-primary ideals in dimension 2 Cohen-Macaulay local rings. As a consequence of this characterisation, he obtained a new proof of Lipman's theorem about product of complete ideals in 2-dimensional rational singularities.

Itoh and Huneke explored this theme further. Itoh proved that the third normal Hilbert coefficient of the maximal ideal m in R in a Gorenstein local ring vanishes if and only if the normal reduction number of m is at most 2. He conjectured in 1992 that this result is true for all m-primary ideals in Gorenstein local rings. We shall discuss a similar criterion for higher normal Hilbert coefficients.