Sung Rak Choi, On the Thresholds of Potential Pairs


Sung Rak Choi
Yonsei Univ.
Choi-Park first introduced and develped the notion of potential pairs. The notion was designed to control the singularities of the outcome of the ‘anticanonical’ minimal model program. In this talk, after reviewing the properties of potnetial klt pairs, we examine the ACC property of the potential lc thresholds. This talk is based on the joint work in progress with Sungwook Jang.

Sung Rak Choi, Subadditivity of Okounkov Bodies


Sung Rak Choi
Yonsei University

We will investigate the subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As an application, we obtain the subadditivity of the numerical Kodaira dimension and the restricted volume for algebraic fiber spaces. As a byproduct, we obtain a criterion of birational isotriviality in terms of Okounkov bodies when the general fiber is of general type. As a special case, we prove some variants of the Iitaka conjecture. We expect that our results will provide a new approach toward the Iitaka conjecture.

This is an ongoing research, in collaboration with Dr. Jinhyung Park.

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