On the blowup of affine spaces along monomial ideals: Tameness

摘要

A tame ideal is an ideal I subset of k[x(1), ..., x(n)] such that the blowup of the affine space 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 complete d-partite d-uniform clutter. Equivalently, 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. (C) 2018 Elsevier Ltd. All rights reserved.