Lipschitz Normal Embeddings and Determinantal Singularities

Helge Møller Pedersen; Maria Aparecida Soares Ruas

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arXiv · 1607.07746

Lipschitz Normal Embeddings and Determinantal Singularities

Helge Møller Pedersen·Maria Aparecida Soares Ruas

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Abstract

The germ of an algebraic variety is naturally equipped with two different metrics up to bilipschitz equivalence. The inner metric and the outer metric. One calls a germ of a variety Lipschitz normally embedded if the two metrics are bilipschitz equivalent. In this article we prove that the model determinantal singularity, that is the space of $m\times n$ matrices of rank less than a given number, is Lipschitz normally embedded. We will also discuss some of the difficulties extending this result to the case of general determinantal singularities.

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BibTeX RIS

Helge Møller Pedersen, Maria Aparecida Soares Ruas. 2016-07-26. Lipschitz Normal Embeddings and Determinantal Singularities. https://arxiv.org/abs/1607.07746

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