Newton-okounkov polytopes of schubert varieties arising from cluster structures

Naoki Fujita; Hironori Oya

Newton-okounkov polytopes of schubert varieties arising from cluster structures

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

MSC Codes 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary)

Original language	English
Journal	Unknown Journal
Publication status	Published - 2020 Feb 23

Keywords

Cluster algebra
Nakashima-Zelevinsky polytope
Newton-Okounkov body
String polytope
Toric degeneration

ASJC Scopus subject areas

General

Fingerprint Dive into the research topics of 'Newton-okounkov polytopes of schubert varieties arising from cluster structures'. Together they form a unique fingerprint.

Cite this

@article{5e456fcff7824cdba78f41aca3951104,

title = "Newton-okounkov polytopes of schubert varieties arising from cluster structures",

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.MSC Codes 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary)",

keywords = "Cluster algebra, Nakashima-Zelevinsky polytope, Newton-Okounkov body, String polytope, Toric degeneration",

author = "Naoki Fujita and Hironori Oya",

year = "2020",

month = feb,

day = "23",

language = "English",

journal = "Unknown Journal",

}

TY - JOUR

T1 - Newton-okounkov polytopes of schubert varieties arising from cluster structures

AU - Fujita, Naoki

AU - Oya, Hironori

PY - 2020/2/23

Y1 - 2020/2/23

N2 - 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.MSC Codes 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary)

AB - 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.MSC Codes 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary)

KW - Cluster algebra

KW - Nakashima-Zelevinsky polytope

KW - Newton-Okounkov body

KW - String polytope

KW - Toric degeneration

UR - http://www.scopus.com/inward/record.url?scp=85095297433&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85095297433&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85095297433

JO - Unknown Journal

JF - Unknown Journal

ER -