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October 13, 2025Open Access

Towards non-commutative crepant resolutions of affine toric Gorenstein varieties

Key Points

Non-commutative crepant resolutions are established for specific affine toric Gorenstein varieties, enhancing the understanding of their geometry.
Results include a generalization based on prior works, enabling new methods for constructing resolutions associated with polytopes.
The analysis focuses on reflexive polytopes with up to $ ext{dim } P + 2$ vertices, revealing the conditions under which resolutions exist.
The study builds on existing literature, indicating a deeper interplay between geometry and algebraic constructs in non-commutative resolutions.

Abstract

In this paper we prove a common generalisation of results by Špenko-Van den Bergh and Iyama-Wemyss that can be used to generate non-commutative crepant resolutions (NCCRs) of some affine toric Gorenstein varieties. We use and generalise results by Novaković to study NCCRs for affine toric Gorenstein varieties associated to cones over polytopes with interior points. As a special case, we consider the case where the polytope is reflexive with P+2 vertices, using results of Borisov and Hua to show the existence of NCCRs.

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Cite This Study

Malter et al. (Mon,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0956a https://doi.org/https://doi.org/10.48550/arxiv.2509.11664

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