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arXiv · 1408.5541

Artin-Nagata properties, minimal multiplicities, and depth of fiber cones

Jonathan Montaño
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Abstract

Minimal values of multiplicities of ideals have a strong relation with the depth of blowup algebras. In this paper, we introduce the notion of Goto-minimal $j$-multiplicity for ideals of maximal analytic spread. In a Cohen-Macaulay ring, inspired by the work of S. Goto, A. Jayanthan, T. Puthenpurakal, and J. Verma, we study the interplay among this new notion, the notion of minimal $j$-multiplicity introduced by C. Polini and Y. Xie, and the Cohen-Macaulayness of the fiber cone of ideals satisfying certain residual assumptions. We are also able to provide a bound on the reduction number of ideals of Goto-minimal $j$-multiplicity having either Cohen-Macaulay associated graded algebra, or linear decay in the depth of their powers.

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Jonathan Montaño. 2014-08-24. Artin-Nagata properties, minimal multiplicities, and depth of fiber cones. https://arxiv.org/abs/1408.5541

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