Article

Determinantal Facet Ideals

• Takayuki Hibi
The Michigan Mathematical Journal (Impact Factor: 0.6). 08/2011; DOI: 10.1307/mmj/1363958240
Source: arXiv

ABSTRACT We consider ideals generated by general sets of $m$-minors of an $m\times n$-matrix of indeterminates. The generators are identified with the facets of
an $(m-1)$-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 $\Delta$, we discuss the question
when the generating minors of its determinantal facet ideal $J_\Delta$ form a
Gr\"obner basis and when $J_\Delta$ is a prime ideal.

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Article: Prime splittings of Determinantal Ideals
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ABSTRACT: We consider determinantal facet ideals i.e., ideals generated by those minors of a generic matrix corresponding to facets of simplicial complexes. Using these ideals we give a combinatorial description for minimal primes of some mixed determinantal ideals. At the end, we discuss the minimal free resolution of these ideals.
08/2012;