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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
25/2020

Toric varieties from cyclic matrix groups

Francesco Galuppi and Mima Stanojkovski

Abstract

We study cyclic groups and semigroups of matrices from an algebraic geometric viewpoint. We prove that the irreducible components of their Zariski closures are toric varieties and study their geometry. In many cases, we are also able to determine their ideal or, in other words, we find all polynomials that vanish on such groups or semigroups. We present an implementation of our results in SageMath.

Received:
Feb 7, 2020
Published:
Feb 10, 2020
MSC Codes:
14M25, 20G20

Related publications

inJournal
2021 Journal Open Access
Francesco Galuppi and Mima Stanojkovski

Toric varieties from cyclic matrix semigroups

In: Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 53 (2021), p. 17