On Burch’s inequality and a reduction system of a filtration

Kinoshita, Y.; Nishida, K.; Yamanaka, Y.; Yoneda, A.

doi:10.1090/S0002-9939-06-08429-2

On Burch’s inequality and a reduction system of a filtration
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by Y. Kinoshita, K. Nishida, Y. Yamanaka and A. Yoneda PDF

Proc. Amer. Math. Soc. 134 (2006), 3437-3444 Request permission

Abstract:

Let $\mathcal {F} = \{ F_n \}$ be a multiplicative filtration of a local ring such that the Rees algebra $\mathrm {R}(\mathcal {F})$ is Noetherian. We recall Burch’s inequality for $\mathcal {F}$ and give an upper bound of the a-invariant of the associated graded ring $\mathrm {a}(\mathrm {G}(\mathcal {F}))$ using a reduction system of $\mathcal {F}$. Applying those results, we study the symbolic Rees algebra of certain ideals of dimension $2$.

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