### Bounds for Hilbert coefficients

Thời gian: 14:00 đến 15:30 Ngày 19/03/2019

Địa điểm: C2-714, VIASM

Báo cáo viên: PGS. TS. Cao Huy Linh

Tóm tắt:

Let $(A, \mm)$ be a noetherian local ring of dimension $d\geq 2$ and $\depth(A) \geq d-1$. Let $I$ be an $\mm$-primary ideal of $A$. Elias proved that  $\depth(G(I^k))$ is constant for $k \gg 0$ and denoted this number by $\sigma(I)$.

In this talk, we investigate  the non-negativity and non-positivity for the Hilbert coefficients of $I$ under assumption  $\sigma(I) \geq d-2$. In case of $I = Q$ is a parameter  ideal, we establish bounds for the Hilbert coefficients of $Q$ in terms of dimension and the first Hilbert coefficients $e_1(Q)$