A note on non-reduced Picard schemes
A note on non-reduced Picard schemes
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关于非简化皮卡德方案的注释
DOI：
10.1016/j.jpaa.2008.09.001
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发表时间：
2008
影响因子：
0.8
通讯作者：
C. Liedtke
中科院分区：
文献类型：
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作者：
C. Liedtke
简化了光滑曲线和光滑复变的皮卡德格式。在这篇笔记中，我们讨论了根据Enriques-Kodaira分类，哪些类别的曲面可以具有非约简皮卡德格式，以及地面场的特征是否存在限制。结果表明，在Kodaira维数κ≤0时，非约简Picard格式是不常见的，这种现象对于κ=2（一般类型）是有界的，对于κ=1也是如此。
The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques–Kodaira classification can have non-reduced Picard schemes and whether there are restrictions on the characteristic of the ground field. It turns out that non-reduced Picard schemes are uncommon in Kodaira dimension κ≤0, that this phenomenon can be bounded for κ=2 (general type) and that it is as bad as can be for κ=1.