Newton-Okounkov polytopes of Schubert varieties arising from cluster structures
arXiv:2002.09912 · doi:10.1090/btran/231
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.
v1 55 pages; v2 57 pages. Section 7 in v1 was removed, and the corresponding results are explained in Sections 5 and 6 in v2, since the statement of Theorem 7.5 in v1 is now known to be true in the symmetrizable case. Section 7 in v2 was added; v3 60 pages. Remark 8.5, Proposition 8.6 and several examples were added. Minor typos were corrected. Final version
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