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arXiv · 1203.5578

Variation of Hilbert Coefficients

L. Ghezzi·S. Goto·J. Hong·W. V. Vasconcelos
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Abstract

For a Noetherian local ring $(\RR, \m)$, the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an $\m$-primary ideal $I$ are known to code for properties of $\RR$, of the blowup of $\spec(\RR)$ 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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L. Ghezzi, S. Goto, J. Hong, W. V. Vasconcelos. 2012-03-26. Variation of Hilbert Coefficients. https://arxiv.org/abs/1203.5578

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