Toric varieties from cyclic matrix groups

Francesco Galuppi and Mima Stanojkovski

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Submission date: 07. Feb. 2020
Pages: 14
Bibtex
MSC-Numbers: 14M25, 20G20
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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.