ON CORRESPONDENCES BETWEEN K3 SURFACES
ON CORRESPONDENCES BETWEEN K3 SURFACES
复制标题
K3 表面之间的对应关系
DOI：
10.1070/im1988v030n02abeh001018
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
V. Nikulin
中科院分区：
文献类型：
--
作者：
V. Nikulin
利用积分二次型的算法和Mukai的结果，证明了C上的K3曲面的上同格在Q上的自同态是由一个代数循环诱导的（如[2]中所推测的），前提是曲面X的Picard格SX表示零（特别是当rk SX≥5时）。在此之前，Mukai在rk SX≥11的假设下得到了这个结果。参考书目：7篇。
Using arithmetic of integral quadratic forms and results of Mukai, it is proved among other things that an endomorphism over Q of the cohomology lattice of a K3 surface over C preserving the Hodge structure and the intersection form is induced by an algebraic cycle (as was conjectured in [2]) provided that the Picard lattice SX of the surface X represents zero (in particular, this is so if rk SX≥5). Previously this result was obtained by Mukai under the assumption that rk SX≥11. Bibliography: 7 titles.