Searcharxiv⌕ Search

arXiv subjects

DongSeon Hwang

Publications and source records attributed to DongSeon Hwang.

At least 19 recordsLinked to original sources
arXiv2026

Automorphism groups of toroidal horospherical varieties

We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure roots of toric fibers that extend to the total space. In particular, we provide a criterion for the reductivity of the connected automorphism groups of such varieties. As an application, we prove the K-unstability of certain $\mathbb{P}^1$-bundles over rational homogeneous spaces.

math.AG↗
arXiv2025

On K-stability of Fano's last Fanos

We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^5$ along a conic. We also describe the automorphism groups of these threefolds.

math.AG↗
arXiv2024

Toric Fano manifolds that do not admit extremal K\"ahler metrics

We show that there exists a toric Fano manifold of dimension $10$ that does not admit an extremal K\"ahler metric in the first Chern class, answering a question of Mabuchi. By taking a product with a suitable toric Fano manifold, one can also produce a toric Fano manifold of dimension $n$ admitting no extremal K\"ahler metric in the first Chern class for each $n \geq 11$.

math.AG↗
arXiv2024

Symmetric and Kähler--Einstein Fano polygons

We investigate \emph{singular} symmetric and Kähler--Einstein Fano polytopes. More precisely, we show that every symmetric Fano polytope is Kähler--Einstein generalizing the work by Batyrev and Selivanova, and study the automorphism groups of symmetric and Kähler--Einstein Fano polygons in detail. In particular, every finte subgroup of $GL_2(\mathbb{Z})$ is an automorphism group of a Kähler--Einstein Fano polygon.

math.AG↗
arXiv2024

Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII

The wonderful compactification $X_m$ of a symmetric homogeneous space of type AIII$(2,m)$ for each $m \geq 4$ is Fano, and its blowup $Y_m$ along the unique closed orbit is Fano if $m \geq 5$ and Calabi-Yau if $m = 4$. Using a combinatorial criterion for K-polystability of smooth Fano spherical varieties obtained by Delcroix, we prove that $X_m$ admits a Kähler-Einstein metric for each $m \geq 4$ and $Y_m$ admits a Kähler-Einstein metric if and only if $m = 4, 5$.

math.AG↗
arXiv2023

Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one

A horospherical variety is a normal $G$-variety such that a connected reductive algebraic group $G$ acts with an open orbit isomorphic to a torus bundle over a rational homogeneous manifold. The projective horospherical manifolds of Picard number one are classified by Pasquier, and it turned out that the automorphism groups of all nonhomogeneous ones are non-reductive, which implies that they admit no Kähler--Einstein metrics. As a numerical measure of the extent to which a Fano manifold is close to be Kähler--Einstein, we compute the greatest Ricci lower bounds of projective horospherical manifolds of Picard number one using the barycenter of each moment polytope with respect to the Duistermaat--Heckman measure based on a recent work of Delcroix and Hultgren. In particular, the greatest Ricci lower bound of the odd symplectic Grassmannian $\text{SGr}(n,2n+1)$ can be arbitrarily close to zero as $n$ grows.

math.AG↗
arXiv2021

W-translated Schubert divisors and transversal intersections

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety of Lie type A via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including complex Grassmannian Gr(2, n) and complete flag variety Fl_4.

math.AG↗
arXiv2021

Algebraic Montgomery-Yang problem and cascade conjecture

The conjecture called algebraic Montgomery-Yang problem is still open for rational $\mathbb{Q}$-homology projective planes with cyclic quotient singularities having ample canonical divisor. All known such surfaces have a special birational behavior called a cascade. In this note, we establish algebraic Montgomery-Yang problem assuming the cascade conjecture, which claims that every rational $\mathbb{Q}$-homology projective planes with quotient singularities having ample canonical divisor admits a cascade.

math.AG↗
arXiv2020

On Barycentric transformations of Fano polytopes

We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be Kähler-Einstein. In particular, we expect that every Kähler-Einstein or symmetric Fano polytope is of type $B_\infty$. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope $X$ of dimension $1$, $3$ or $5$, $X$ is Kähler-Einstein if and only if it is of type $B_\infty$.

math.AG↗
arXiv2020

Cascades of toric log del Pezzo surfaces of Picard number one

We classify toric log del Pezzo surfaces of Picard number one by introducing the notion, cascades. As an application, we show that if such a surface is Kähler-Einstein, then it should admit a special cascade, and it satisfies the equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e., $K^2 = 3e_{orb}.$

math.AG↗
arXiv2017

A Note on Rational Cuspidal curves on $\mathbb{Q}$-Homology Projective Planes

We generalize results by Wakabayashi and Orevkov about rational cuspidal curves on the projective plane to that on $\mathbb{Q}$-homology projective planes. It turns out that the result is exactly the same as the projective plane case under suitable assumptions. We also provide examples which demonstrate sharpness of the results. The ambient surface is singular in these examples.

math.AG↗
arXiv2015

Gorenstein $\mathbb{Q}$-homology projective planes

We present the complete list of all singularity types on Gorenstein $\mathbb{Q}$-homology projective planes, i.e., normal projective surfaces of second Betti number one with at worst rational double points. The list consists of $58$ possible singularity types, each except two types supported by an example.

math.AG↗
arXiv2014

Factorization of anticanonical maps of Fano type varieties

The purpose of the present paper is to generalize Sakai's work on anticanonical models of rational surfaces to varieties of Fano type. We first prove a characterization of Fano type varieties using the singularities of anticanonical models. Secondly, we study the decomposition of the anticanonical map using the $K_X$-minimal model program.

math.AG↗
arXiv2014

Cox rings of rational surfaces and redundant blow-ups

We prove that the redundant blow-up preserves the finite generation of the Cox ring of a rational surface under a suitable assumption, and we study the birational structure of Mori dream rational surfaces via redundant blow-ups. It turns out that the redundant blow-up completely characterizes birational morphisms of Mori dream rational surfaces with anticanonical Iitaka dimension $0$. As an application, we construct new Mori dream rational surfaces with anticanonical Iitaka dimension $0$ and $-\infty$ of arbitrarily large Picard number.

math.AG↗
arXiv2014

Redundant blow-ups of rational surfaces with big anticanonical divisor

We completely classify redundant blow-ups appearing in the theory of rational surfaces with big anticanonical divisor due to Sakai. In particular, we construct a rational surface with big anticanonical divisor which is not a minimal resolution of a del Pezzo surface with only rational singularities, which gives a negative answer to a question raised in a paper by Testa, Várilly-Alvarado, and Velasco.

math.AG↗
arXiv2013

Characterization of log del Pezzo pairs via anticanonical models

There are several variations of the definition of log del Pezzo pairs in the literature. We define their suitable smooth models, and we show that they are the same. In particular, we obtain a characterization of smooth log del Pezzo pairs in terms of anticanonical models. As applications, we classify non-rational weak log canonical del Pezzo pairs, and we prove that every surface of globally F-regular type is of Fano type.

math.AG↗
arXiv2011

Algebraic Montgomery-Yang Problem: the noncyclic case

Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere ${\mathbb S}^5$ has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with quotient singularities such that $b_2(S) = 1$ has at most 3 singular points if its smooth locus $S^0$ is simply-connected. In this paper, we prove the conjecture under the assumption that $S$ has at least one noncyclic singularity. In the course of the proof, we classify projective surfaces $S$ with quotient singularities such that (i) $b_2(S) = 1$, (ii) $H_1(S^0, \mathbb{Z}) = 0$, and (iii) $S$ has 4 or more singular points, not all cyclic, and prove that all such surfaces have $π_1(S^0)\cong \mathfrak{A}_5$, the icosahedral group.

math.AG↗