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On reduced arc spaces of toric varieties

Ilya Dumanski, Evgeny Feigin, Ievgen Makedonskyi and Igor Makhlin

Vol. 19 (2025), No. 2, 313–363
DOI: 10.2140/ant.2025.19.313
Abstract

An arc space of an affine cone over a projective toric variety is known to be nonreduced in general. It was demonstrated recently that the reduced scheme structure of arc spaces is very meaningful from algebro-geometric, representation-theoretic and combinatorial points of view. 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.

Keywords
arc spaces, toric varieties
Mathematical Subject Classification
Primary: 05E14, 14E18
Milestones
Received: 19 September 2022
Revised: 29 February 2024
Accepted: 29 April 2024
Published: 31 January 2025
Authors
Ilya Dumanski
Faculty of Mathematics
HSE University
Moscow
Russia
Evgeny Feigin
School of Mathematical Sciences
Tel Aviv University
Tel Aviv
Israel
Ievgen Makedonskyi
Faculty of Mathematics and Computer Science
Friedrich Schiller Jena University
Germany
Beijing Institute of Mathematical Sciences and Applications
Beijing
China
Igor Makhlin
Technische Universität Berlin
Berlin
Germany

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