论文标题
在3倍FANO纤维上的分隔线的非理性界限
Bounding non-rationality of divisors on 3-fold Fano fibrations
论文作者
论文摘要
在本文中，我们研究了在轻度条件下的3倍对数Fano纤维$（x，b）\ z $的非理性分隔线的非理性性。我们表明，如果$ d $是$ b $的一部分，其系数$ \ ge t> 0 $，该$在$ z $上签约，那么$ d $ to $ \ mathbb {p}^1 \ times c $，其中$ c $在仅在$ t $上限制的，$ c $是一种平稳的投射曲线。此外，如果$ t> \ frac {1} {2} $，则$ c $的属仅取决于$ t $。
In this paper we investigate non-rationality of divisors on 3-fold log Fano fibrations $(X,B)\to Z$ under mild conditions. We show that if $D$ is a component of $B$ with coefficient $\ge t>0$ which is contracted to a point on $Z$, then $D$ is birational to $\mathbb{P}^1\times C$ where $C$ is a smooth projective curve with gonality bounded depending only on $t$. Moreover, if $t>\frac{1}{2}$, then genus of $C$ is bounded depending only on $t$.
