On the splitting of Lazarsfeld-Mukai bundles on K3 surfaces II
On the splitting of Lazarsfeld-Mukai bundles on K3 surfaces II
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K3 表面上 Lazarsfeld-Mukai 束的分裂 II
DOI：
10.1016/j.jalgebra.2018.09.042
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发表时间：
2019
影响因子：
0.9
通讯作者：
Watanabe Kenta
中科院分区：
文献类型：
--
作者：
Izuru Mori and Kenta Ueyama;Watanabe Kenta;Izuru Mori;Watanabe Kenta
在以前的工作中，我们在一个数值条件下，给出了K3曲面X上秩为2的Lazarssen-Mukai丛由两个线丛的扩张给出的一个必要条件（[10]，定理3.1）。在P3（[10]，命题3.1）中，当X是光滑四次超曲面时，我们将出现在这种扩张中的线丛分类为它的一个推论，但它的断言有一些错误。本文对它们进行了修正，并给出了文[10]中结果的一个应用.
In the previous works, we gave a necessary condition for Lazarsfeld–Mukai bundles of rank 2 on a K3 surface X to be given by an extension of two line bundles, under a numerical condition ([10], Theorem 3.1). Moreover, we have classified line bundles which appear in such an extension, in the case where X is a smooth quartic hypersurface in P 3 ([10], Proposition 3.1) as a corollary of it. However, the assertion of it contains a few mistakes. In this paper, we correct them, and give an application of the results in [10].