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arXiv · 1407.1493

Local Cohomology of Multi-Rees Algebras with Applications to Joint Reductions and Complete Ideals

Shreedevi K. Masuti·Tony J. Puthenpurakal·J. K. Verma
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Abstract

In this paper, we obtain a generalization, in dimension $3$, of a theorem of David Rees about joint reductions of the bigraded filtration $\{ \overline{I^rJ^s}\}$ of complete ${\mathfrak m}$-primary ideals and vanishing of the second normal Hilbert coefficient $\overline{e}_2(IJ)$ where $R$ is a two-dimensional Cohen-Macaulay analytically unramified local ring with maximal ideal $\mathfrak m.$ This generalization is obtained as a consequence of a formula for the third local cohomology module of the extended Rees algebras of the $\mathbb Z^3$-graded filtration $\{\overline{I^rJ^sK^t}\}$ with support in the ideal $(x_1t_1,x_2t_2,x_3t_3)$ where $(x_1,x_2,x_3)$ is a good joint reduction of $\{\overline{I^rJ^sK^t}\}.$

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Shreedevi K. Masuti, Tony J. Puthenpurakal, J. K. Verma. 2014-07-06. Local Cohomology of Multi-Rees Algebras with Applications to Joint Reductions and Complete Ideals. https://arxiv.org/abs/1407.1493

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