论文标题
关于拉回抛物线矢量束的稳定性
On the stability of pulled back parabolic vector bundles
论文作者
论文摘要
采用在特征零的代数封闭字段上定义的不可约的光滑投影曲线$ x $，并确定其有限的许多独特点$ d \，= \，\ {x_1，\，\，\ cdots，\ cdots，\，\，x_n \} $;对于每个点$ x \，\ in \，d $修复正整数$ n_x $。从不可约的光滑投影曲线中获取非稳定地图$ f \，：\，y \，\ longrightArrow \，x $。我们使用$（d，d，\，\，\ {n_x \} _ {x \ {x \ in d}）构建了一个天然子捆$ \ Mathcal {f} \，\ subset \，f _*{\ Mathcal O} _y $ $。令$ e _*$为稳定的抛物线矢量束，其每个$ x \，\ in \ in \，d $在$ \ frac {1} {n_x} $中的积分倍数。我们证明，如果$ {\ rm rank}（\ Mathcal {f}）\，= \，1 $，请抛物$ f^*e _*$也是抛物线稳定的。
Take an irreducible smooth projective curve $X$ defined over an algebraically closed field of characteristic zero, and fix finitely many distinct point $D\, =\, \{x_1,\, \cdots,\, x_n\}$ of it; for each point $x\, \in\, D$ fix a positive integer $N_x$. Take a nonconstant map $f\, :\, Y\, \longrightarrow \, X$ from an irreducible smooth projective curve. We construct a natural subbundle $\mathcal{F}\, \subset\, f_*{\mathcal O}_Y$ using $(D,\, \{N_x\}_{x\in D})$. Let $E_*$ be a stable parabolic vector bundle whose parabolic weights at each $x\, \in\, D$ are integral multiples of $\frac{1}{N_x}$. We prove that the pullback $f^*E_*$ is also parabolic stable, if ${\rm rank}(\mathcal{F})\,=\, 1$.
