Bounding the First Hilbert Coefficient

Details Bounding the First Hilbert Coefficient Bounding the First Hilbert Coefficient

2011-05-11

arxiv.org/abs/1105.2325v1

Mathematics

Commutative Algebra

11 pages

Scientific paper

This paper gives new bounds on the first Hilbert coefficient of an ideal of
finite colength in a Cohen-Macaulay local ring. The bound given is quadratic in
the multiplicity of the ideal. We compare our bound to previously known bounds,
and give examples to show that at least in some cases it is sharp. The
techniques come largely from work of Elias, Rossi, Valla, and Vasconcelos.

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