On the splitting of Lazarsfeld-Mukai bundles on K3 surfaces

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• 作者：Kenta Watanabe ^{goo314kenta@mail.goo.ne.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：ACM line bundle ; Lazarsfeld&ndash ; Mukai bundle ; K3 surface ; Donagi&ndash ; Morrison's extension
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：447
• 期：Complete
• 页码：445-454
• 全文大小：271 K

文摘

Let X be a K3 surface, let C be a smooth curve on X, and let Z be a base point free pencil on C  . Then, the Lazarsfeld–Mukai bundle 627" title="Click to view the MathML source">E_C,Z$E_{C,Z}$ of rank 2 associated with C and Z   is given by an extension of the torsion free sheaf J_Z⊗O_X(C)${\mathcal{J}}_Z\otimes {\mathcal{O}}_X(C)$ by 6212ee37950f63" title="Click to view the MathML source">O_X${\mathcal{O}}_X$, where J_Z${\mathcal{J}}_Z$ is the ideal sheaf of Z in X. We can see that if C is very ample as a divisor on X  , 627" title="Click to view the MathML source">E_C,Z$E_{C,Z}$ is an ACM bundle with respect to 2c1290b51d25de" title="Click to view the MathML source">O_X(C)${\mathcal{O}}_X(C)$. In this paper, by using this fact, we will characterize a necessary condition for 627" title="Click to view the MathML source">E_C,Z$E_{C,Z}$ to be given by an extension of two line bundles on X  , by ACM line bundles with respect to 2c1290b51d25de" title="Click to view the MathML source">O_X(C)${\mathcal{O}}_X(C)$.