Invariance of plurigenera for generalized polarized pairs with abundant nef parts

凯勒簇的多重典范类形变不变性的若干方面

Aspects of deformation invariance of plurigenera of Kähler varieties

该研究结合准则与凯勒极小模型纲领，证明了凯勒族多重典范类等的多项形变不变性结果，并将广义极化对的相关不变性结论从射影族推广至莫伊谢佐恩族。

Nef and abundant divisors, semiampleness and canonical bundle formula

In this paper, we use canonical bundle formulas to prove some generalizations of an old theorem of Kawamata on the semiampleness of nef and abundant log canonical divisors. In particular, we show that for klt pairs $(X,B)$ with $K_X+B$ effective, $L \in Pic (X)$ nef, nefness and abundance of $K_X+B+L$ implies semiampleness. This essentially generalizes Kawamata's theorem to the setting of generalized abundance.

On generalized lc pairs with $\mathrm{\textbf b}$-log abundant nef part

We study the behavior of generalized lc pairs with $\mathrm{\textbf b}$-log abundant nef part, a meticulously designed structure on algebraic varieties. We show that this structure is preserved under the canonical bundle formula and sub-adjunction formulas, and is also compatible with the non-vanishing conjecture and the abundance conjecture in the classical minimal model program.

Note on the semiampleness theorem for the log canonical divisors on klt varieties which are nef and abundant

We give another alternative proof to the Kawamata semiampleness theorem for the log canonical divisors on klt varieties which are nef and abundant. After the first version of this article was posted to the e-print Arxiv, Prof. Fujino notified the author that the quick and essential proof ([Fujino. On Kawamata's theorem.(EMS 2011), Rem 2.7]) is already known. The author would like to thank him. More precisely, Prof. Fujino already gave the quick and essential proof ([Fujino. On Kawamata's thm.(EMS 2011), Rem 2.7], [Fujino. Finite generation of the lc ring in dim 4. (Kyoto J. Math. 50 (2010)), R…

Asymptotic base loci on singular varieties

We prove that the non-nef locus and the restricted base locus of a pseudoeffective divisor coincide on KLT pairs. We also extend to KLT pairs F. Russo's characterization of nef and abundant divisors by means of asymptotic multiplier ideals.

广义对的半丰富性

Semiampleness for generalized pairs

本文证明了广义 klt 对在典范除子 nef 且丰富的条件下具有半丰富性，并进一步建立了广义无基点定理。