论文标题
Kähler品种的$ 4 $维度最小模型程序
On the $4$-dimensional minimal model program for Kähler varieties
论文作者
论文摘要
在本文中，我们建立以下结果：令$（x，b）$为DLT对，其中$ x $是$ \ m artbb q $ -tactorialkähler$ 4 $ -fold - （i）如果$ x $紧凑，并且$ k_x+k_x+b \ sim _ {\ sim _ {\ nathb Q} d \ geq quq quq quq 0 $ b）$ b）$ b） a log minimal model, (ii) if $(X/T, B)$ is a semi-stable klt pair, $W\subset T$ a compact subset and $K_X+B$ is effective over $W$ (resp. not effective over $W$), then we can run a $(K_X+B)$-MMP over $T$ (in a neighborhood of $W$) which ends with a minimal model over $T$ (resp. a Mori超过$ t $）的光纤空间。我们还提供了在各个维度中存在分析品种的翻转的证明，以及分析品种之间的射向形态的相对MMP。
In this article we establish the following results: Let $(X, B)$ be a dlt pair, where $X$ is a $\mathbb Q$-factorial Kähler $4$-fold -- (i) if $X$ is compact and $K_X+B\sim_{\mathbb Q} D\geq 0$ for some effective $\mathbb Q$-divisor, then $(X, B)$ has a log minimal model, (ii) if $(X/T, B)$ is a semi-stable klt pair, $W\subset T$ a compact subset and $K_X+B$ is effective over $W$ (resp. not effective over $W$), then we can run a $(K_X+B)$-MMP over $T$ (in a neighborhood of $W$) which ends with a minimal model over $T$ (resp. a Mori fiber space over $T$). We also give a proof of the existence of flips for analytic varieties in all dimensions and the relative MMP for projective morphisms between analytic varieties.
