Journal of Symplectic Geometry

Volume 21 (2023)

Number 3

Unique toric structure on a Fano Bott manifold

Pages: 439 – 462

DOI: https://dx.doi.org/10.4310/JSG.2023.v21.n3.a1

Authors

Yunhyung Cho (Department of Mathematics Education, Sungkyunkwan University, Seoul, South Korea)

Eunjeong Lee (Center for Geometry and Physics, Institute for Basic Science, Pohang, South Korea; and Department of Mathematics, Chungbuk National University, Cheongju, South Korea)

Mikiya Masuda (Osaka City University Advanced Mathematics Institute (OCAMI), and Department of Mathematics, Graduate School of Science, Osaka City University, Osaka, Japan)

Seonjeong Park (Department of Mathematics Education, Jeonju University, Jeonju, South Korea)

Abstract

We prove that if there exists a $c_1$-preserving graded ring isomorphism between integral cohomology rings of two Fano Bott manifolds, then they are isomorphic as toric varieties. As a consequence, we give an affirmative answer to McDuff’s question on the uniqueness of a toric structure on a Fano Bott manifold.

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Received 2 May 2021

Accepted 25 October 2022

Published 22 December 2023