On the blowup of affine spaces along monomial ideals: Tameness. (July 2019)

• Record Type: Journal Article
• Authors: Nasrollah Nejad, Abbas; Nikseresht, Ashkan; Yazdan Pour, Ali Akbar; Zaare-Nahandi, Rashid
• Is Part Of: Journal of symbolic computation. Volume 93(2019)
• Page Start: 85
• Page End: 99
• Publication Date: 2019-07
• Subjects: primary 14M25 14E15 13A30 -- secondary 13F55 14B05; Blowup algebra -- Resolution of singularity -- Tame ideal -- Clutter; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.04.009
• Languages: English
• ISSNs: 0747-7171

Abstract

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.