CW-resolutions of monomial ideals that are supported on face posets

ABSTRACT

Given a monomial ideal I with minimal free resolution ℱ supported in characteristic p>0 on a CW-complex X with regular 2-skeleton, in general it is not the case that the face poset of X, P(X), also supports ℱ in the sense of Clark and Tchernev. We construct a (not necessarily regular) CW-complex Y that also supports ℱ and such that the face poset P(Y) also supports ℱ.

KEYWORDS:

• Commutative algebra
• CW-resolutions
• minimal free resolutions
• monomial ideals

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Commutative Algebra: 13-XX
• Homological Algebra: 18Gxx
• Homotopy Theory: 14F35
• Combinatorics: 05-XX

Acknowledgment

The author would like to thank both Alexandre Tchernev and Marco Varisco for their helpful discussions and insights.