6 papers
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 …
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…
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…
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 \(E_2\)…
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.
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.