On the blowup of affine spaces along monomial ideals: Tameness. (July 2019) - Nasrollah Nejad, Abbas; Nikseresht, Ashkan; Yazdan Pour, Ali Akbar; Zaare-Nahandi, Rashid
Abstract: A tame ideal is an ideal I ⊂ 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.