Seonjeong Park

activity

20102026

most citedCohomological rigidity of manifolds defined by right-angled 3-dimensional polytopes

34 citations · 71 across the 24 of their papers we have counts for

collaborators

29 papers

math.CO2026

Permutation module decomposition of the cohomology of Hessenberg varieties associated with lollipop graphs

Soojin Cho, Seonjeong Park

We study the cohomology of regular semisimple Hessenberg varieties associated with lollipop graphs as a module under the dot action. Using the natural basis introduced by Cho, Hong…

math.AG2025

Intersections of Schubert varieties and smooth $T$ -stable subvarieties of flag varieties

Jaehyun Hong, Eunjeong Lee, Seonjeong Park

A smooth projective variety equipped with a suitable torus action admits a cell decomposition, called the Białynicki-Birula decomposition. The singularities of the closures of thes…

math.AG2023

Toric Schubert varieties and directed Dynkin diagrams

Eunjeong Lee, Mikiya Masuda, Seonjeong Park

A flag variety is a homogenous variety $G / B$ where $G$ is a simple algebraic group over the complex numbers and $B$ is a Boel subgroup of $G$ . A Schubert variety $X_{w}$ is a subvari…

math.AG2023

$c_{1}$ -cohomological rigidity for smooth toric Fano varieties of Picard number two

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda +1

The $c_{1}$ -cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a $c_{1}$ -preserving isomorphism between their integra…

math.CO2023

Towards combinatorial characterization of the smoothness of Hessenberg Schubert varieties

Soojin Cho, JiSun Huh, Seonjeong Park

A \emph{Hessenberg Schubert variety} is an irreducible component of the intersection of a Schubert variety and a Hessenberg variety, defined as the closure of a Schubert cell inter…

math.AG2022

Toric varieties of Schröder type

JiSun Huh, Seonjeong Park

A dissection of a polygon is obtained by drawing diagonals such that no two diagonals intersect in their interiors. In this paper, we define a toric variety of Schröder type as a s…

math.AG2022

Torus orbit closures in the flag variety

Eunjeong Lee, Mikiya Masuda, Seonjeong Park

The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and Gelfand--Serganova in the mid-1980s, but it seems that not much has been done since t…

math.AG2021

On the enumeration of Fano Bott manifolds

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda +1

Fano Bott manifolds bijectively correspond to signed rooted forests with some equivalence relation. Using this bijective correspondence, we enumerate the isomorphism classes of Fan…

math.AT2021

Conic decomposition of a toric variety and its application to cohomology

Seonjeong Park, Jongbaek Song

We introduce the notion of a \emph{conic sequence} of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain re…

math.AG2021

Toric Richardson varieties of Catalan type and Wedderburn-Etherington numbers

Eunjeong Lee, Mikiya Masuda, Seonjeong Park

We associate a complete non-singular fan with a polygon triangulation. Such a fan appears from a certain toric Richardson variety, called of Catalan type introduced in this paper.…

math.AT2020★ 4 cited

On Schubert varieties of complexity one

Eunjeong Lee, Mikiya Masuda, Seonjeong Park

Let $B$ be a Borel subgroup of $GL_{n} (C)$ and $T$ a maximal torus contained in $B$ . Then $T$ acts on $GL_{n} (C) / B$ and every Sc…

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.AT2020

Poincare polynomials of generic torus orbit closures in Schubert varieties

Eunjeong Lee, Mikiya Masuda, Seonjeong Park +1

The closure of a generic torus orbit in the flag variety $G / B$ of type $A$ is known to be a permutohedral variety and its Poincare polynomial agrees with the Eulerian polynomial. I…

math.CO2019

Torus orbit closures in flag varieties and retractions on Weyl groups

Eunjeong Lee, Mikiya Masuda, Seonjeong Park

A finite Coxeter group $W$ has a natural metric $d$ and if $M$ is a subset of $W$ , then for each $u \in W$ , there is $q \in M$ such that $d (u, q) = d (u, M)$ …

math.CO2019★ 13 cited

Toric Bruhat interval polytopes

Eunjeong Lee, Mikiya Masuda, Seonjeong Park

For two elements $v$ and $w$ of the symmetric group $S_{n}$ with $v \leq w$ in Bruhat order, the Bruhat interval polytope $Q_{v, w}$ is the convex hull of the points $(z(1),…

math.AG2018

The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope

Megumi Harada, Tatsuya Horiguchi, Mikiya Masuda +1

Regular semisimple Hessenberg varieties are subvarieties of the flag variety $Flag (C^{n})$ arising naturally in the intersection of geometry, representation theory,…

math.CO2018★ 4 cited

Graph invariants and Betti numbers of real toric manifolds

Boram Park, Hanchul Park, Seonjeong Park

For a graph $G$ , a graph cubeahedron $□_{G}$ and a graph associahedron $△_{G}$ are simple convex polytopes which admit (real) toric manifolds. In this paper, we introduce…

math.AT2017

Toric manifolds over cyclohedra

Seonjeong Park

We study the action of the dihedral group on the (equivariant) cohomology of the toric manifolds associated with cycle graphs.

math.AT2017★ 2 cited

Classification of toric manifolds over an $n$ -cube with one vertex cut

Sho Hasui, Hideya Kuwata, Mikiya Masuda +1

We say that a complete nonsingular toric variety (called a toric manifold in this paper) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with…

math.CO2017★ 2 cited

On shellability for a poset of even subgraphs of a graph

Boram Park, Seonjeong Park

Given a simple graph $G$ , a poset of its even subgraphs was firstly considered by S. Choi and H. Park to study the topology of a real toric manifold associated with $G$ . S. Choi an…

math.AT2016★ 34 cited

Cohomological rigidity of manifolds defined by right-angled 3-dimensional polytopes

Victor Buchstaber, Nikolay Erokhovets, Mikiya Masuda +2

A family of closed manifolds is called cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. We establish cohomologic…

math.AT2015

Pseudograph and its associated real toric manifold

Suyoung Choi, Boram Park, Seonjeong Park

Given a simple graph $G$ , the graph associahedron $P_{G}$ is a convex polytope whose facets correspond to the connected induced subgraphs of $G$ . Graph associahedra have been studied…

math.AT2014

Toric origami structures on quasitoric manifolds

Anton Ayzenberg, Mikiya Masuda, Seonjeong Park +1

We construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold. All necessary topological definitions and combin…

math.AT2014★ 5 cited

Cohomology of toric origami manifolds with acyclic proper faces

Anton Ayzenberg, Mikiya Masuda, Seonjeong Park +1

A toric origami manifold is a generalization of a symplectic toric manifold (or a toric symplectic manifold). The origami symplectic form is allowed to degenerate in a good control…

Permutation module decomposition of the cohomology of Hessenberg varieties associated with lollipop graphs

Intersections of Schubert varieties and smooth T-stable subvarieties of flag varieties

Toric Schubert varieties and directed Dynkin diagrams

c1​-cohomological rigidity for smooth toric Fano varieties of Picard number two

Towards combinatorial characterization of the smoothness of Hessenberg Schubert varieties

Toric varieties of Schröder type

Torus orbit closures in the flag variety

On the enumeration of Fano Bott manifolds

Conic decomposition of a toric variety and its application to cohomology

Toric Richardson varieties of Catalan type and Wedderburn-Etherington numbers

On Schubert varieties of complexity one

Unique toric structure on a Fano Bott manifold

Poincare polynomials of generic torus orbit closures in Schubert varieties

Torus orbit closures in flag varieties and retractions on Weyl groups

Toric Bruhat interval polytopes

The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope

Graph invariants and Betti numbers of real toric manifolds

Toric manifolds over cyclohedra

Classification of toric manifolds over an n-cube with one vertex cut

On shellability for a poset of even subgraphs of a graph

Cohomological rigidity of manifolds defined by right-angled 3-dimensional polytopes

Pseudograph and its associated real toric manifold

Toric origami structures on quasitoric manifolds

Cohomology of toric origami manifolds with acyclic proper faces

Intersections of Schubert varieties and smooth $T$ -stable subvarieties of flag varieties

$c_{1}$ -cohomological rigidity for smooth toric Fano varieties of Picard number two

Classification of toric manifolds over an $n$ -cube with one vertex cut