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September 11, 2026
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Polyhedral Models for K-Theory of Toric and Flag Varieties

Seminaire Lotharingien de Combinatoire. 2023. Vol. 89B. Article 76.
Leonid Monin, Smirnov E.

In 1992, Pukhlikov and Khovanskii provided a description of the cohomology ring of toric variety as a quotient of the ring of differential operators on spaces of virtual polytopes. Later Kaveh generalized this construction to the case of cohomology rings for full flag varieties.

In this paper we extend Pukhlikov--Khovanskii type presentation to the case of K-theory of toric and flag varieties. First we study the Gorenstein duality quotients of the group algebra of free abelian group (possibly of infinite rank). Then we specialize to the K-ring of integer (virtual) polytopes with a fixed normal fan. Finally we show that the K-theory of toric and flag varieties can be realized as polytope K-rings and describe the classes of toric orbits or Schubert varieties in them.

Research target: Mathematics
Language: English
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Keywords: многообразие флаговtoric varietyторическое многообразиеK-Theoryflag varietyK-теория
Publication based on the results of:
Motivic, categoric and classical algebraic geometry, and its connection to differential geometry of special manifolds (2023)
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