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arXiv · 2208.10432

On reduced arc spaces of toric varieties

Ilya Dumanski·Evgeny Feigin·Ievgen Makedonskyi·Igor Makhlin
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Abstract

An arc space of an affine cone over a projective toric variety is known to be non-reduced in general. It was demonstrated recently that the reduced scheme structure is worth studying due to various connections with representation theory and combinatorics. In this paper we develop a general machinery for the description of the reduced arc spaces of affine cones over toric varieties. We apply our techniques to a number of classical cases and explore some connections with representation theory of current algebras.

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Ilya Dumanski, Evgeny Feigin, Ievgen Makedonskyi, Igor Makhlin. 2022-08-22. On reduced arc spaces of toric varieties. https://doi.org/10.2140/ant.2025.19.313

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