# Examples of k-regular maps and interpolation spaces

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**Examples of k-regular maps and interpolation spaces.** / Michalek, Mateusz; Miller, Chris.

Research output: Contribution to journal › Article › Scientific › peer-review

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

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*Linear Algebra and Its Applications*,

*530*, 94-108. https://doi.org/10.1016/j.laa.2017.05.003

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TY - JOUR

T1 - Examples of k-regular maps and interpolation spaces

AU - Michalek, Mateusz

AU - Miller, Chris

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Interpolation spaces

KW - k-regular map

KW - Areole

KW - GORENSTEIN LOCI

U2 - 10.1016/j.laa.2017.05.003

DO - 10.1016/j.laa.2017.05.003

M3 - Article

VL - 530

SP - 94

EP - 108

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 30273252