A note on linear resolution and polymatroidal ideals

2018/10/17 by Mafi, Amir, Naderi, Dler
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.07582

Abstract

Let R=K[x₁,...,x_n] be the polynomial ring in n variables over a field K and I be a monomial ideal generated in degree d. Bandari and Herzog conjectured that a monomial ideal I is polymatroidal if and only if all its monomial localizations have a linear resolution. In this paper we give an affirmative answer to the conjecture in the following cases: (i) \rm height(I)=n-1; (ii) I contains at least n-3 pure powers of the variables x₁^d,...,x_n-3^d; (iii) I is a monomial ideal in at most four variables.

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