On the isotriviality of families of elliptic surfaces
On the isotriviality of families of elliptic surfaces
复制标题
论椭圆曲面族的等平凡性
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
E. Viehweg
中科院分区：
文献类型：
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作者：
K. Oguiso;E. Viehweg
研究了复射影曲线上Kodaira维数为1的椭圆曲面的非等平凡射影族。如果基底是一条椭圆曲线，我们证明家族必须有一个单一的纤维，并且在投影线上它必须至少有三个单一的纤维。对于一般类型的曲面族，Migliorini和Kov'acs已经得到了类似的结果，他们以Kodaira维数为零的投影曲面族而闻名。修订版：我们修正了一些小错误和歧义，并完成了参考文献列表。
We study non-isotrivial projective families of elliptic surfaces of Kodaira dimension one, over complex projective curves. If the base is an elliptic curve, we show that the family must have a singular fibre, and that over the projective line it must have at least three singular fibres. Similar results, for families of surfaces of general type, have been obtained by Migliorini and Kov'acs, and they are well-known for projective families of surfaces of Kodaira dimension zero. Revised version: We corrected some minor errors and ambiguities, and we completed the list of references.