Variation of Hilbert coefficients

Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer

doi:10.1090/S0002-9939-2013-11774-0

Variation of Hilbert coefficients
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by Laura Ghezzi, Shiro Goto, Jooyoun Hong and Wolmer V. Vasconcelos PDF

Proc. Amer. Math. Soc. 141 (2013), 3037-3048 Request permission

Abstract:

For a Noetherian local ring $(\mathbf {R}, \mathfrak {m})$, the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an $\mathfrak {m}$-primary ideal $I$ are known to code for properties of $\mathbf {R}$, of the blowup of $\operatorname {Spec}(\mathbf {R})$ along $V(I)$, and even of their normalizations. We give estimations for these coefficients when $I$ is enlarged (in the case of $e_1$ in the same integral closure class) for general Noetherian local rings.

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