TL;DR
This paper presents a novel perspective by describing the Taylor and Lyubeznik resolutions as simplicial resolutions, revealing that the Scarf complex is the intersection of all minimal free resolutions of a monomial ideal.
Contribution
It introduces a new simplicial interpretation of classical resolutions and characterizes the Scarf complex as the intersection of all minimal free resolutions.
Findings
Taylor and Lyubeznik resolutions are simplicial resolutions
Scarf complex equals the intersection of all minimal free resolutions
Provides a new perspective on resolutions of monomial ideals
Abstract
We describe the Taylor and Lyubeznik resolutions as simplicial resolutions, and use them to show that the Scarf complex of a monomial ideal is the intersection of all its minimal free resolutions.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation