Examples of k-regular maps and interpolation spaces

Mateusz Michalek, Chris Miller

Research output: Contribution to journalArticleScientificpeer-review

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 languageEnglish
Pages (from-to)94-108
Number of pages15
JournalLinear Algebra and Its Applications
Volume530
DOIs
Publication statusPublished - 1 Oct 2017
MoE publication typeA1 Journal article-refereed

Keywords

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

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