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.
05-12-18

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Abstract

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.