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Schubert Calculus on Newton–Okounkov Polytopes

P. 233–249.
Kiritchenko V., Padalko M.

A Newton–Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent Schubert cycles by linear combinations of faces of the polytope so that the intersection product of cycles corresponds to the set-theoretic intersection of faces (whenever the latter are transverse). We explain the general framework and survey particular realizations of this approach in types A, B and C.

Language: English
Full text
DOI
Keywords: исчисление ШубертаSchubert calculusмногогранники Гельфанда–Цетлинаgeometric mitosisгеометрический митозGelfand-Zetlin polytopes
Publication based on the results of:
Motivic, categoric and classical algebraic geometry, and its connection to differential geometry of special manifolds (2023)

In book

Interactions with Lattice Polytopes Magdeburg, Germany, September 2017
Springer, 2022.
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