论文标题
$ \ mathbb {p}^3 $和lazarsfeld-mukai捆绑包的四分之一超曲面的ACM捆绑
ACM bundles of rank 2 on quartic hypersurfaces in $\mathbb{P}^3$ and Lazarsfeld-Mukai bundles
论文作者
论文摘要
令$ x $为$ \ mathbb {p}^3 $中的平滑四分之一的超曲面。通过Brill-Noether在K3表面上的曲线理论，如果全球生成$ x $上的排名2 ACM捆绑包，那么它是Lazarsfeld-Mukai Bundle $ e_ e_ {c，Z} $与$ x $上的平滑曲线$ c $相关的$ x $和base Point Point free Pline Poline $ z $ z $ c $ c $ c $。在本文中，我们将重点介绍$ x $上的此类捆绑包，以调查$ x $的ACM排名第2套。具体而言，我们将为排名2的$ e_ {c，z} $的等级2矢量束提供必要的条件，以不可混合初始化和ACM，如果$ c $ in PIC中的$ c $（$ x $）包含在$ x $ $ x $ $ x $的$ x $ and-trivial intrivial Initialized Acmimitized Acm cun $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x中。
Let $X$ be a smooth quartic hypersurface in $\mathbb{P}^3$. By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on $X$ is globally generated, then it is the Lazarsfeld-Mukai bundle $E_{C,Z}$ associated with a smooth curve $C$ on $X$ and a base point free pencil $Z$ on $C$. In this paper, we will focus on the classification of such bundles on $X$ to investigate aCM bundles of rank 2 on $X$. Concretely, we will give a necessary condition for a rank 2 vector bundle of type $E_{C,Z}$ to be indecomposable initialized and aCM, in the case where the class of $C$ in Pic($X$) is contained in the sublattice of rank 2 generated by the hyperplane class of $X$ and a non-trivial initialized aCM line bundle on $X$.
