Dae-Won Lee

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math.AG2025

Minimal model program on the generic fiber of log Calabi-Yau type fibration

Donghyeon Kim, Dae-Won Lee

We study the minimal model program on the geometric generic fiber of a fibration $f : X \to S$ such that for a Zariski dense subset $S^{'} \subseteq S$ , $X_{s}$ is an $ε$ -lc log C…

math.AG2025

A valuative approach to the anticanonical minimal model program

Sung Rak Choi, Sungwook Jang, Donghyeon Kim +1

In this paper, we show that the log canonical threshold of a potentially klt triple can be computed by a quasi-monomial valuation. The notion of potential triples provides a larger…

math.AG2025

On minimal model program and Zariski decomposition of potential triples

Sung Rak Choi, Sungwook Jang, Dae-Won Lee

In this paper, we investigate properties of potential triples $(X, Δ, D)$ which consists of a pair $(X, Δ)$ and a pseudoeffective $R$ -Cartier divisor $D$ . In particular, we s…

math.AG2024

Anticanonical divisor with good asymptotic base loci

Sung Rak Choi, Sungwook Jang, Dae-Won Lee

In this paper, we give a characterization of Fano type varieties in terms of the asymptotic base loci of $- (K_{X} + Δ)$ . We also show that for a potentially lc pair $(X, Δ)$ , if no plc…