Tame graphs, clutters and their Rees algebras
Abstract
A tame ideal is an ideal I such that the blowup of the affine space Akn 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.
0