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Determinantal Facet Ideals
We consider ideals generated by general sets of -minors of an -matrix of indeterminates. The generators are identified with the facets of
an -dimensional pure simplicial complex. The ideal generated by the
minors corresponding to the facets of such a complex is called a determinantal
facet ideal. Given a pure simplicial complex , we discuss the question
when the generating minors of its determinantal facet ideal form a
Gr\"obner basis and when is a prime ideal
Linear balls and the multiplicity conjecture
A linear ball is a simplicial complex whose geometric realization is
homeomorphic to a ball and whose Stanley--Reisner ring has a linear resolution.
It turns out that the Stanley--Reisner ring of the sphere which is the boundary
complex of a linear ball satisfies the multiplicity conjecture. A class of
shellable spheres arising naturally from commutative algebra whose
Stanley--Reisner rings satisfy the multiplicity conjecture will be presented.Comment: 19 Page
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