11 papers
Mori dream fibers and the geometric generic fiber
Dae-Won Lee, Masaru Nagaoka
We construct a smooth projective family of rational surfaces over . The Mori dream property of a fiber is determined by the torsion of the normal bundle…
Coupled Pklt Tuples and Varieties of Pklt Type
Donghyeon Kim, Dae-Won Lee
We introduce asymptotic multiplier ideal sheaves and log canonical thresholds associated with tuples of pseudoeffective divisors on a projective klt pair. We prove that the thresho…
Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree
Kiryong Chung, Dae-Won Lee
In this paper, we give a complete description of the Hilbert schemes of rational curves up to degree on a prime Fano threefold of degree . One of the key ingredients in…
Flexibility of affine cones over blow-ups of weighted projective planes
In-Kyun Kim, Dae-Won Lee, Masatomo Sawahara
Let be the surface obtained by blowing up at general smooth points, where . For every very ample Cartier divisor on , we prove th…
On the quasi-monomiality of the - and -invariants
Donghyeon Kim, Dae-Won Lee
In this paper, we show that for any projective klt pair over an algebraically closed field of characteristic \(0\) and any big -Cartier -divisor …
Structure of the Anticanonical Minimal Model Program for Potentially klt Pairs
Donghyeon Kim, Dae-Won Lee
We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski d…
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 such that for a Zariski dense subset , is an -lc log C…
Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero
In-Kyun Kim, Dae-Won Lee, Masatomo Sawahara
In this paper, we study the cylindricity of -forms of singular del Pezzo surfaces obtained by blowing up weighted projective planes over an arbitrary fie…
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…
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 which consists of a pair and a pseudoeffective -Cartier divisor . In particular, we s…
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 . We also show that for a potentially lc pair , if no plc…