论文标题
真正的分支地图和稳定的向量捆绑包
Genuinely ramified maps and stable vector bundles
论文作者
论文摘要
令$ f：x \ rightarrow y $是在代数封闭的字段定义的不可还原的普通投影品种之间可分离的有限迁移图，以便of f_*：π_1^{\ rm et}（x）\rightarrowπ_1^^ym ym f_*：π_1^{\ rm et}（x）修复$ y $上的两极分化，并在$ y $上的$ f $ ableck $ x $配备$ x $。给定$ x $上的稳定矢量捆绑包$ e $，我们证明$ f^*w $ y $上有一个矢量捆绑$ w $，而$ f^*w $ isomorphic to $ e $ if to $ e $，并且仅当直接image $ f_*e $包含一个稳定的矢量bundle $ f $ f $ f $ f $ f $ f $ f $ \ frac {1} {{\ rm度}（f）} \ cdot \ frac {{{\ rm度}（e）} {{\ rm strank}（e）} $$我们还证明，$ f^*v $对于每个稳定的bundle bundle bundle bundle bundle bundle bundle $ v $ on $ y $ y $ y都是稳定的。
Let $f : X \rightarrow Y$ be a separable finite surjective map between irreducible normal projective varieties defined over an algebraically closed field, such that the corresponding homomorphism between étale fundamental groups $f_* : π_1^{\rm et}(X)\rightarrowπ_1^{\rm et}(Y)$ is surjective. Fix a polarization on $Y$ and equip $X$ with the pullback, by $f$, of this polarization on $Y$. Given a stable vector bundle $E$ on $X$, we prove that there is a vector bundle $W$ on $Y$ with $f^*W$ isomorphic to $E$ if and only if the direct image $f_*E$ contains a stable vector bundle $F$ such that $$ \frac{{\rm degree}(F)}{{\rm rank}(F)}= \frac{1}{{\rm degree}(f)}\cdot \frac{{\rm degree}(E)}{{\rm rank}(E)} $$ We also prove that $f^*V$ is stable for every stable vector bundle $V$ on $Y$.
