Sparse Systems of Parameters for Determinantal Varieties

Glassbrenner, Donna; Smith, Karen E.

doi:10.1006/aama.1997.0559

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Corollary 42 the Number Of Minimal Components Of1

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“…Glassbrenner and Smith (1997) proved that determinantal varieties have systems of parameters that are highly symmetric and sparse. We now show that this is not the case for (2 × 2)-permanental varieties.…”

Section: Corollary 42 the Number Of Minimal Components Ofmentioning

confidence: 99%

Permanental Ideals

Laubenbacher

Swanson

2000

Journal of Symbolic Computation

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We show that the (2 × 2)-subpermanents of a generic matrix generate an ideal whose height, unmixedness, primary decomposition, the number and structure of the minimal components, resolutions, radical, integral closure and Gröbner bases all depend on the characteristic of the underlying subfield: if the characteristic of the subfield is two, this ideal is the determinantal ideal for which all of these properties are already well known. We show that as long as the characteristic of the subfield is not two, the results are in marked contrast with those for the determinantal ideals.

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Section: Corollary 42 the Number Of Minimal Components Ofmentioning

confidence: 99%