Constructions of k-regular maps using finite local schemes

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

BUCZYŃSKI, Jarosław, Tadeusz JANUSZKIEWICZ, Joachim JELISIEJEW, Mateusz MICHALEK, 2019. Constructions of k-regular maps using finite local schemes. In: Journal of the European Mathematical Society. European Mathematical Society (EMS). 21(6), pp. 1775-1808. ISSN 1435-9855. eISSN 1435-9863. Available under: doi: 10.4171/JEMS/873

@article{Buczynski2019Const-52566, title={Constructions of k-regular maps using finite local schemes}, year={2019}, doi={10.4171/JEMS/873}, number={6}, volume={21}, issn={1435-9855}, journal={Journal of the European Mathematical Society}, pages={1775--1808}, author={Buczyński, Jarosław and Januszkiewicz, Tadeusz and Jelisiejew, Joachim and Michalek, Mateusz} }

Michalek, Mateusz eng 2021-01-26T12:39:47Z 2021-01-26T12:39:47Z Buczyński, Jarosław Jelisiejew, Joachim terms-of-use 2019 A continuous map R<sup>m</sup>→R<sup>N</sup> or C<sup>m</sup>→C<sup>N</sup> is called k-regular if the images of any k points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of N for which such maps exist. The methods of algebraic topology provide lower bounds for N, but there are very few results on the existence of such maps for particular values m and k. Using methods of algebraic geometry we construct k-regular maps. We relate the upper bounds on N with the dimension of the locus of certain Gorenstein schemes in the punctual Hilbert scheme. The computations of the dimension of this family is explicit for k≤9, and we provide explicit examples for k≤5. We also provide upper bounds for arbitrary m and k. Buczyński, Jarosław Januszkiewicz, Tadeusz Constructions of k-regular maps using finite local schemes Januszkiewicz, Tadeusz Jelisiejew, Joachim Michalek, Mateusz

This item appears in the following Collection(s)

Search KOPS


My Account