Donghyeon Kim

collaborators

5 papers

math.AG2026

On volumes and the generic invariance of Fano type varieties

Donghyeon Kim

We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset…

math.AG2026

On the quasi-monomiality of the $I^\pm$ - and $I^´$ -invariants

Donghyeon Kim, Dae-Won Lee

In this paper, we show that for any projective klt pair $(X, I^)$ over an algebraically closed field of characteristic $0$ and any big $Q$ -Cartier $Q$ -divisor $L…

math.AG2026

On the normalized local volume of a non-closed point

Donghyeon Kim

In this note, we show that the normalized local volume of a non-closed point can be expressed in terms of the normalized local volumes of closed points.

math.AG2025

The number of smooth varieties in an MMP on a 3-fold of Fano type

Donghyeon Kim

In this paper, we prove that for a threefold of Fano type $X$ and a movable $Q$ -Cartier Weil divisor $D$ on $X$ , the number of smooth varieties that arise during the runni…

math.AG2025

Asymptotically flat divisors and strongly $F$ -regular type varieties

Donghyeon Kim

In this paper, we define the notion of asymptotically flat divisor on a normal variety over $\C$, and prove that if $X$ is a strongly $F$ -regular type variety and $K_{X}$ is asymptot…

On volumes and the generic invariance of Fano type varieties

On the quasi-monomiality of the I^±- and I^´-invariants

On the normalized local volume of a non-closed point

The number of smooth varieties in an MMP on a 3-fold of Fano type

Asymptotically flat divisors and strongly F-regular type varieties

On the quasi-monomiality of the $I^\pm$ - and $I^´$ -invariants

Asymptotically flat divisors and strongly $F$ -regular type varieties