论文标题
存在具有固定决定因素的可半介绍束
Existence of semistable vector bundles with fixed determinants
论文作者
论文摘要
让$ r $成为一个出色的Henselian离散估值戒指，任何特征的代数封闭的残留物场$ k $。修复整数$ r，d $，带有$ r \ ge 2 $。让$ x_r $是规格（$ r $）的常规纤维表面，特殊纤维表示$ x_k $，$ x_k $，这是一种类似树状的树状曲线$ g \ ge 2 $。令$ {l} _r $为$ d $ $ d $的$ x_r $的行捆绑包，以使$ x_k $的合理组件上$ {l} _r $的限制程度是$ r $的倍数。在本文中，我们证明了$ r $ r $本地免费的捆绑包上的$ x_r $的存在，以确保$ {l} _r $的$ x_r $，因此在纤维上可以半固定。
Let $R$ be an excellent Henselian discrete valuation ring with algebraically closed residue field $k$ of any characteristic. Fix integers $r,d$ with $r\ge 2$. Let $X_R$ be a regular fibred surface over Spec($R$) with special fibre denoted $X_k$, a generalised tree-like curve of genus $g \ge 2$. Let ${L}_R$ be a line bundle on $X_R$ of degree $d$ such that the degree of the restriction of ${L}_R$ on the rational components of $X_k$ is a multiple of $r$. In this article we prove the existence of a rank $r$ locally free sheaf on $X_R$ of determinant ${L}_R$ such that it is semistable on the fibres.
