Self-dual toric varieties

Apostolos Thoma; Marius Vladoiu

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arXiv · 2312.11653

Self-dual toric varieties

Apostolos Thoma·Marius Vladoiu

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Abstract

We describe explicitly all multisets of weights whose defining projective toric varieties are self-dual. In addition, we describe a remarkable and unexpected combinatorial behaviour of the defining ideals of these varieties. The toric ideal of a self-dual projective variety is weakly robust, that means the Graver basis is the union of all minimal binomial generating sets. When, in addition, the self-dual projective variety has a non-pyramidal configuration, then the toric ideal is strongly robust, namely the Graver basis is a minimal generating set, therefore there is only one minimal binomial generating set which is also a reduced Gr\"obner basis with respect to every monomial order and thus, equals the universal Gr\"obner basis.

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BibTeX RIS

Apostolos Thoma, Marius Vladoiu. 2023-12-18. Self-dual toric varieties. https://arxiv.org/abs/2312.11653

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