# Prime splittings of determinantal ideals

@article{Mohammadi2012PrimeSO,
title={Prime splittings of determinantal ideals},
journal={Communications in Algebra},
year={2012},
volume={46},
pages={2278 - 2296}
}
• Published 14 August 2012
• Mathematics
• Communications in Algebra
ABSTRACT We consider determinantal ideals, where the generating minors are encoded in a hypergraph. We study when the generating minors form a Gröbner basis. In this case, the ideal is radical, and we can describe algebraic and numerical invariants of these ideals in terms of combinatorial data of their hypergraphs, such as the clique decomposition. In particular, we can construct a minimal free resolution as a tensor product of the minimal free resolution of their cliques. For several classes…
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