7 citations · 22 across the 12 of their papers we have counts for
14 papers
On subadditivity of Okounkov bodies for algebraic fiber spaces
Sung Rak Choi, Jinhyung Park
The purpose of this paper is to establish a subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As applications, we obtain a product formula of the restricted cano…
Comparing numerical Iitaka dimensions again
Sung Rak Choi, Jinhyung Park
To seek for the useful numerical analogues to the Iitaka dimension, various numerical Iitaka dimensions have been defined from a number of different perspectives. It has been accep…
On a generalized Batyrev's cone conjecture
Sung Rak Choi, Yoshinori Gongyo
We discuss some variants of cone theorem for movable curves in any codimensions.
Local numerical equivalences and Okounkov bodies in higher dimensions
Sung Rak Choi, Jinhyung Park, Joonyeong Won
We continue to explore the numerical nature of the Okounkov bodies focusing on the local behaviors near given points. More precisely, we show that the set of Okounkov bodies of a p…
A product formula for volumes of divisors via Okounkov bodies
Sung Rak Choi, Seung-Jo Jung, Jinhyung Park +1
We generalize Kawamata's product formula for volumes of canonical divisors to arbitrary divisors using Okounkov bodies
Okounkov bodies associated to abundant divisors and Iitaka fibrations
Sung Rak Choi, Jinhyung Park, Joonyeong Won
The aim of this paper is to study the Okounkov bodies associated to abundant divisors. As a main result, we prove that the valuative Okounkov bodies of an abundant divisor encode a…
Okounkov bodies associated to pseudoeffective divisors II
Sung Rak Choi, Jinhyung Park, Joonyeong Won
We first prove some basic properties of Okounkov bodies, and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov…
Okounkov bodies and Zariski decompositions on surfaces
Sung Rak Choi, Jinhyung Park, Joonyeong Won
The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly…
Okounkov bodies associated to pseudoeffective divisors
Sung Rak Choi, Yoonsuk Hyun, Jinhyung Park +1
An Okounkov body is a convex subset in Euclidean space associated to a big divisor on a smooth projective variety with respect to an admissible flag. In this paper, we introduce tw…
Asymptotic base loci via Okounkov bodies
Sung Rak Choi, Yoonsuk Hyun, Jinhyung Park +1
An Okounkov body is a convex subset of Euclidean space associated to a divisor on a smooth projective variety with respect to an admissible flag. In this paper, we recover the asym…
Potentially non-klt locus and its applications
Sung Rak Choi, Jinhyung Park
We introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor. The potentially non-klt locus is a subset of which…
Factorization of anticanonical maps of Fano type varieties
Sung Rak Choi, DongSeon Hwang, Jinhyung Park
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 typ…
On the dual of the mobile cone
Sung Rak Choi
We prove that the cone of mobile divisors and the cone of curves birationally movable in codimension 1 are dual in the -negative part for a klt pair . We also prove…
Geography of log models:theory and applications
Sung Rak Choi, Vyacheslav Shokurov
An introduction to geography of log models with applications to positive cones of FT varieties and to geometry of minimal models and Mori fibrations.