Yunhyung Cho

activity

20102026

most citedOn the f-vectors of Gelfand-Cetlin polytopes

26 citations · 70 across the 33 of their papers we have counts for

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23 papers · 1 filter

math.SG2024

Cluster algebras and monotone Lagrangian tori

Yunhyung Cho, Myungho Kim, Yoosik Kim +1

Motivated by the construction of Newton--Okounkov bodies and toric degenerations via cluster algebras in [GHKK18, FO25], we consider a family of Newton--Okounkov polytopes of a com…

math.SG2020★ 1 cited

Unique toric structure on a Fano Bott manifold

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda +1

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.…

math.SG2019

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Yunhyung Cho

Let $(M, ω_{M})$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^{1}$ -action. We show that $(M, ω_{M})$ is $S^{1}$ -equivariant symplec…

math.SG2019★ 3 cited

A critical point analysis of Landau--Ginzburg potentials with bulk in Gelfand--Cetlin systems

Yunhyung Cho, Yoosik Kim, Yong-Geun Oh

Using the bulk-deformation of Floer cohomology by Schubert cycles and non-Archimedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential function, we prove that every comp…

math.SG2019

Remark on the Betti numbers for Hamiltonian circle actions

Yunhyung Cho

In this paper, we establish a certain inequality in terms of Betti numbers of a closed Hamiltonian $S^{1}$ -manifold with isolated fixed points.

math.SG2019

Lagrangian fibers of Gelfand-Cetlin systems

Yunhyung Cho, Yoosik Kim, Yong-Geun Oh

A Gelfand-Cetlin system is a completely integrable system defined on a partial flag manifold whose image is a rational convex polytope called a Gelfand-Cetlin polytope. Motivated b…

math.SG2019

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions III

Yunhyung Cho

In this paper, we complete the classification of six-dimensional closed monotone symplectic manifolds admitting semifree Hamiltonian $S^{1}$ -actions. We also show that every such man…

math.SG2019

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions II

Yunhyung Cho

Let $(M, ω_{M})$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^{1}$ -action. We show that if the maximal and the minimal fixed c…

math.SG2018

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I

Yunhyung Cho

Let $(M, ω_{M})$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^{1}$ -action. We show that if the minimal (or maximal) fixed comp…

math.SG2018★ 1 cited

Lagrangian fibers of Gelfand--Cetlin systems of $SO (n)$ -type

Yunhyung Cho, Yoosik Kim

In this paper, we study the Gelfand--Cetlin systems and polytopes of the co-adjoint $SO (n)$ -orbits. We describe the face structure of Gelfand--Cetlin polytopes and iterate…

math.SG2018★ 5 cited

Monotone Lagrangians in flag varieties

Yunhyung Cho, Yoosik Kim

In this paper, we give a formula for the Maslov index of a gradient holomorphic disc, which is a relative version of the Chern number formula of a gradient holomorphic sphere for a…

math.SG2017★ 12 cited

Lagrangian fibers of Gelfand-Cetlin systems

Yunhyung Cho, Yoosik Kim, Yong-Geun Oh

Motivated by the study of Nishinou-Nohara-Ueda on the Floer thoery of Gelfand-Cetlin systems over complex partial flag manifolds, we provide a complete description of the topology…

math.SG2016

On the Chern numbers for pseudo-free circle actions

Byung Hee An, Yunhyung Cho

Let $(M, ψ)$ be a $(2 n + 1)$ -dimensional oriented closed manifold equipped with a pseudo-free $S^{1}$ -action $ψ : S^{1} \times M \to M$ . We first define a \textit{local data} $\mat…

math.SG2014

Unimodality of the Betti numbers for Hamiltonian circle actions with index-increasing moment maps

Yunhyung Cho

The unimodality conjecture posed by Tolman in the conference `Moment maps in Various Geometry" in 2005 states that if (M,w) is a 2n-dimensional smooth compact symplectic manifold e…

math.SG2014★ 2 cited

Hard Lefschetz property of symplectic structures on compact Kaehler manifolds

Yunhyung Cho

In this paper, we give a new method to construct a compact symplectic manifold which does not satisfy the hard Lefschetz property. Using our method, we construct a simply connected…

math.SG2013

Hamiltonian circle action with self-indexing moment map

Yunhyung Cho, Min Kyu Kim

Let $(M, ω)$ be a $2 n$ -dimensional smooth compact symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points and let $μ : M \to R$ be a co…

math.SG2013★ 1 cited

Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds

Yunhyung Cho, Min Kyu Kim

In this paper, we study the hard Lefschetz property of a symplectic manifold which admits a Hamiltonian torus action. More precisely, let $(M, ω)$ be a 6-dimensional compact symplec…

math.SG2013

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Yunhyung Cho, Min Kyu Kim

Let $(M, ω)$ be an eight-dimensional closed symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points. In this article, we will show that the Bet…

math.SG2013★ 1 cited

An example of circle actions on symplectic Calabi-Yau manifolds with non-empty fixed points

Yunhyung Cho, Min Kyu Kim

Let $(X, σ, J)$ be a compact Kähler Calabi-Yau manifold equipped with a symplectic circle action. By Frankel's theorem \cite{F}, the action on $X$ is non-Hamiltonian and $X$ does not…

math.SG2012★ 2 cited

Embedded surfaces for symplectic circle actions

Yunhyung Cho, Min Kyu Kim, Dong Youp Suh

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precise…

math.SG2011

Log-concavity of complexity one Hamiltonian torus actions

Yunhyung Cho, Min Kyu Kim

Let $(M, ω)$ be a closed $2 n$ -dimensional symplectic manifold equipped with a Hamiltonian $T^{n - 1}$ -action. Then Atiyah-Guillemin-Sternberg convexity theorem implies that the image…

math.SG2011★ 2 cited

The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points

Yunhyung Cho

Let $(M, ω)$ be a closed $2 n$ -dimensional semifree Hamiltonian $S^{1}$ -manifold with only isolated fixed points. We prove that a density function of the Duistermaat-Heckman measure is…

math.SG2010★ 7 cited

Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set

Yunhyung Cho, Taekgyu Hwang, Dong Youp Suh

Let $(M, ω)$ be a 6-dimensional closed symplectic manifold with a symplectic $S^{1}$ -action with $M^{S^{1}} \neq = \emptyset$ and $dim M^{S^{1}} \leq 2$ . Assume that $ω$ is integral with…

Cluster algebras and monotone Lagrangian tori

Unique toric structure on a Fano Bott manifold

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

A critical point analysis of Landau--Ginzburg potentials with bulk in Gelfand--Cetlin systems

Remark on the Betti numbers for Hamiltonian circle actions

Lagrangian fibers of Gelfand-Cetlin systems

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions III

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions II

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I

Lagrangian fibers of Gelfand--Cetlin systems of SO(n)-type

Monotone Lagrangians in flag varieties

Lagrangian fibers of Gelfand-Cetlin systems

On the Chern numbers for pseudo-free circle actions

Unimodality of the Betti numbers for Hamiltonian circle actions with index-increasing moment maps

Hard Lefschetz property of symplectic structures on compact Kaehler manifolds

Hamiltonian circle action with self-indexing moment map

Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

An example of circle actions on symplectic Calabi-Yau manifolds with non-empty fixed points

Embedded surfaces for symplectic circle actions

Log-concavity of complexity one Hamiltonian torus actions

The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points

Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set

Lagrangian fibers of Gelfand--Cetlin systems of $SO (n)$ -type