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arXiv · 2002.09912

Newton-Okounkov polytopes of Schubert varieties arising from cluster structures

Naoki Fujita·Hironori Oya
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Abstract

The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton-Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton-Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima-Zelevinsky polytopes.

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BibTeXRIS

Naoki Fujita, Hironori Oya. 2020-02-23. Newton-Okounkov polytopes of Schubert varieties arising from cluster structures. https://doi.org/10.1090/btran%2F231

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