In-Kyun Kim

activity

20152026

most citedAlpha invariants of birationally rigid Fano threefolds

3 citations · 9 across the 18 of their papers we have counts for

collaborators

20 papers

math.DG2026

Sasaki-Einstein metrics on connected sums of $S^{3} \times S^{4}$

Dasol Jeong, In-Kyun Kim, Jihun Park +1

We completely characterize the $n$ -fold connected sums of $S^{3} \times S^{4}$ that admit Sasaki-Einstein structures by proving that such a structure exists if and only if $n$ is even.

math.AG2026

Polarized cylinders on blow-ups of weighted projective planes

In-Kyun Kim, Masatomo Sawahara, Joonyeong Won

We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m + 4$ …

math.AG2026

Cylinders in weighted Fano varieties

Adrien Dubouloz, In-Kyun Kim, Takashi Kishimoto +1

Cylinders in Fano varieties receives a lot of attentions recently from the viewpoints of birational geometry and unipotent geometry. In this article, we provide a survey of several…

math.AG2025

Automorphism groups and cylindricity of weighted hypersurface Fano threefolds

In-Kyun Kim, Takashi Kishimoto, Joonyeong Won

It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano ind…

math.AG2025

K-stability of del Pezzo surfaces with a single quotient singularity

In-Kyun Kim, Dae-Won Lee

In this paper, we study the K-stability of del Pezzo surfaces with a single quotient singularity whose minimal resolution admits exactly two exceptional curves $E_1$ and $E_2$…

math.AG2025

Rigid affine cones over singular del Pezzo surfaces

In-Kyun Kim, Jaehyun Kim, Joonyeong Won

We completely determine the existence of anticanonical polar cylinders in quasi-smooth log del Pezzo surfaces of index one.

math.AG2023

K-polystability of the first secant varieties of rational normal curves

In-Kyun Kim, Jinhyung Park, Joonyeong Won

The first secant variety $Σ$ of a rational normal curve of degree $d \geq 3$ is known to be a $Q$ -Fano threefold. In this paper, we prove that $Σ$ is K-polystable, and hen…

math.AG2023

K-unstable singular del Pezzo surfaces without anticanonical polar cylinder

In-Kyun Kim, Jaehyun Kim, Joonyeong Won

We prove the existence of singular del Pezzo surfaces that are neither K-semistable nor contain any anticanonical polar cylinder.

math.DG2022

New Sasaki-Einstein 5-manifolds

Dasol Jeong, In-Kyun Kim, Jihun Park +1

We prove that closed simply connected $5$ -manifolds $2 (S^{2} \times S^{3}) # n M_{2}$ allow Sasaki-Einstein structures, where $M_{2}$ is the closed simply connected $5$ -manifold with $\mathr…

math.AG2022

K-stability of log del Pezzo hypersurfaces with index 2

In-Kyun Kim, Nivedita Viswanathan, Joonyeong Won

We completely classify K-stability of log del Pezzo hypersurfaces with index 2.

math.CV2021

Briançon-Skoda exponents and the maximal root of reduced Bernstein-Sato polynomials

Seung-Jo Jung, In-Kyun Kim, Morihiko Saito +1

For a holomorphic function $f$ on a complex manifold $X$ , the Briançon-Skoda exponent $e^{BS} (f)$ is the smallest integer $k$ with $f^{k} \in (\partial f)$ (replacing $X$ with a ne…

math.AG2021

Higher Du Bois singularities of hypersurfaces

Seung-Jo Jung, In-Kyun Kim, Morihiko Saito +1

For a complex algebraic variety $X$ , we introduce higher $p$ -Du Bois singularity by imposing canonical isomorphisms between the sheaves of Kähler differential forms $Ω_{X}^{q}$ and the…

math.AG2020★ 1 cited

Unstable singular del Pezzo hypersurfaces with lower index

In-kyun Kim, Joonyeong Won

We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.

math.AG2020★ 2 cited

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

In-Kyun Kim, Takuzo Okada, Joonyeong Won

We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$ . Combining this with the result of Stibitz and…

math.AG2019★ 1 cited

Hodge ideals and spectrum of isolated hypersurface singularities

Seung-Jo Jung, In-Kyun Kim, Morihiko Saito +1

We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$ -filtration modulo the Jacobian ideal…

math.AG2019★ 1 cited

Alpha invariants of birationally bi-rigid Fano 3-folds I

In-Kyun Kim, Takuzo Okada, Joonyeong Won

We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove…

math.AG2018★ 1 cited

Hodge ideal and spectrum of weighted homogeneous isolated singularities

Seung-Jo Jung, In-Kyun Kim, Youngho Yoon

This note provides a connection between the Hodge spectrum and the Hodge ideals recently developed by Mustaţǎ--Popa in the case of weighted homogeneous isolated singularities.

math.AG2018

Global log canonical thresholds of minimal $(1, 2)$ -surfaces

In-Kyun Kim, YongJoo Shin, Joonyeong Won

Let $S$ be a minimal surface of general type with $p_{g} (S) = 2$ and $K_{S}^{2} = 1$ , so called by a minimal $(1, 2)$ -surface. Then we obtain that the global log canonical threshold of the su…

math.AG2016★ 3 cited

Alpha invariants of birationally rigid Fano threefolds

In-Kyun Kim, Takuzo Okada, Joonyeong Won

We compute global log canonical thresholds, or equivalently alpha invariants, of birationally rigid orbifold Fano threefolds embedded in weighted projective spaces as codimension t…

math.AG2015

All complete intersection varieties are Fano visitors

Young-Hoon Kiem, In-Kyun Kim, Hwayoung Lee +1

We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This e…

Sasaki-Einstein metrics on connected sums of S3×S4

Polarized cylinders on blow-ups of weighted projective planes

Cylinders in weighted Fano varieties

Automorphism groups and cylindricity of weighted hypersurface Fano threefolds

K-stability of del Pezzo surfaces with a single quotient singularity

Rigid affine cones over singular del Pezzo surfaces

K-polystability of the first secant varieties of rational normal curves

K-unstable singular del Pezzo surfaces without anticanonical polar cylinder

New Sasaki-Einstein 5-manifolds

K-stability of log del Pezzo hypersurfaces with index 2

Briançon-Skoda exponents and the maximal root of reduced Bernstein-Sato polynomials

Higher Du Bois singularities of hypersurfaces

Unstable singular del Pezzo hypersurfaces with lower index

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

Hodge ideals and spectrum of isolated hypersurface singularities

Alpha invariants of birationally bi-rigid Fano 3-folds I

Hodge ideal and spectrum of weighted homogeneous isolated singularities

Global log canonical thresholds of minimal (1,2)-surfaces

Alpha invariants of birationally rigid Fano threefolds

All complete intersection varieties are Fano visitors

Sasaki-Einstein metrics on connected sums of $S^{3} \times S^{4}$

Global log canonical thresholds of minimal $(1, 2)$ -surfaces