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arXiv · 1602.02431

Tame graphs, clutters and their Rees algebras

Abbas Nasrollah Nejad·Ashkan Nikseresht·Ali Akbar Yazdan Pour·Rashid Zaare-Nahandi
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Abstract

A tame ideal is an ideal $I$ such that the blowup of the affine space $\mathbb{A}_k^n$ along $I$ is regular. In this paper, we give a combinatorial characterization of tame squarefree monomial ideals. More precisely, we show that a square free monomial ideal is tame if and only if the corresponding clutter is a union of some isolated vertices and a complete $d$-partite $d$-uniform clutter. It turns out that a squarefree monomial ideal is tame, if and only if the facets of its Stanley-Reisner complex have mutually disjoint complements. Also, we characterize all monomial ideals generated in degree at most 2 which are tame. Finally, we prove that tame squarefree ideals are of fiber type.

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Abbas Nasrollah Nejad, Ashkan Nikseresht, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi. 2016-02-07. Tame graphs, clutters and their Rees algebras. https://arxiv.org/abs/1602.02431

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