Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
46/2018

Coordinate-wise Powers of Algebraic Varieties

Papri Dey, Paul Görlach and Nidhi Kaihnsa

Abstract

We introduce and study coordinate-wise powers of subvarieties of $\mathbb{P}^n$, i.e.\ varieties arising from raising all points in a given subvariety of $\mathbb{P}^n$ to the $r$-th power, coordinate by coordinate. This corresponds to studying the image of a subvariety of $\mathbb{P}^n$ under the quotient of $\mathbb{P}^n$ by the action of the finite group $\mathbb{Z}_r^{n+1}$. We determine the degree of coordinate-wise powers and study their defining equations, particularly for hypersurfaces and linear spaces. Applying these results, we compute the degree of the variety of orthostochastic matrices and determine iterated dual and reciprocal varieties of power sum hypersurfaces. We also establish a link between coordinatewise squares of linear spaces and the study of real symmetric matrices with a degenerate eigenspectrum.

Received:
Jul 10, 2018
Published:
Jul 10, 2018

Related publications

inJournal
2020 Journal Open Access
Papri Dey, Paul Görlach and Nidhi Kaihnsa

Coordinate-wise powers of algebraic varieties

In: Beiträge zur Algebra und Geometrie, 61 (2020) 3, pp. 473-505