General K3 surfaces obtained as double covers of the n -th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K 3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

中文翻译：

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Hirzebruch曲面的双重覆盖K3曲面

作为n = 0、1、4的第n个Hirzebruch曲面的双重覆盖而获得的常规K3曲面不是其他光滑曲面的双重覆盖。我们基于双重覆盖的分支轨迹和Hirzebruch表面的纤维空间，给出了这样一个K 3表面是另一个光滑有理表面的双重覆盖的判据。