Vasconcelos' uniformity conjecture for Chern coefficients

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Let (R,m)(R,\mathfrak{m}) be a Noetherian local ring, let II be an m\mathfrak{m}-primary ideal, and let A\mathcal{A} be an II-good filtration. Vasconcelos' uniformity conjecture. There exist functions fl(I)f_l(I) and fu(I)f_u(I) defined with extended degree over RR such that

fl(I)≤e1(A)≤fu(I).f_l(I)\leq \mathrm{e}_{1}(\mathcal{A})\leq f_u(I).

The conjecture seeks uniform lower and upper bounds for the first Hilbert coefficient of good filtrations in terms of extended degree.

References

Primary source

Jooyoun Hong and Susan Morey, “Hilbert Coefficients and Sally Modules: A Survey of Vasconcelos' Contributions”, arXiv:2312.06846 (2023).

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