Face rings of complexes with singularities
Isabella Novik, Ed Swartz
TL;DR
This paper characterizes when the face ring of a pure simplicial complex modulo generic linear forms has finite local cohomology, linking this property to the nonsingularity of links of faces of certain dimensions.
Contribution
It provides a precise criterion connecting the algebraic property of the face ring to the topological property of links in the simplicial complex.
Findings
Face ring modulo m linear forms has finite local cohomology iff links of faces of dimension ≥ m are nonsingular.
Establishes a link between algebraic properties of face rings and topological features of simplicial complexes.
Offers a characterization that can be used to identify complexes with desired algebraic properties.
Abstract
It is shown that the face ring of a pure simplicial complex modulo generic linear forms is a ring with finite local cohomology if and only if the link of every face of dimension or more is nonsingular.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory