### Abstract

A continuous map f : C-n -> C-N is k-regular if the image of any k distinct points spans a k-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev, to construct k-regular maps with small N, and only a few nontrivial examples are known so far. Applying tools from algebraic geometry we construct a 4-regular polynomial map C-3 -> C-11 and a 5-regular polynomial map C-3 -> C-14. (C) 2017 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 94-108 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 530 |

DOIs | |

Publication status | Published - 1 Oct 2017 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- Interpolation spaces
- k-regular map
- Areole
- GORENSTEIN LOCI

## Cite this

Michalek, M., & Miller, C. (2017). Examples of k-regular maps and interpolation spaces.

*Linear Algebra and Its Applications*,*530*, 94-108. https://doi.org/10.1016/j.laa.2017.05.003