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arXiv · 1710.11189

Determinacy of Determinantal Varieties

Imran Ahmed·Maria Aparecida Soares Ruas
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Abstract

A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of a $m\times n$-matrix. In this note, we consider $\mathcal{G}$-finite determinacy of matrices defining a special class of determinantal varieties. They are called essentially isolated determinantal singularities (EIDS) and were defined by Ebeling and Gusein-Zade. In this note, we prove that matrices parametrized by generic homogeneous forms of degree $d$ define EIDS. It follows that $\mathcal{G}$-finite determinacy of matrices hold in general. As a consequence, EIDS of a given type $(m,n,t)$ holds in general.

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Imran Ahmed, Maria Aparecida Soares Ruas. 2017-10-30. Determinacy of Determinantal Varieties. https://doi.org/10.1007/s00229-018-1041-0

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