Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fiber bundles. They are known to have positive signature divisible by [Formula: see text]. Examples are known only with signature 16 and more. We review approaches to construct examples of low signature which admit two independent fibrations. Special attention is paid to ramified covers of product of curves which we analyze by studying the monodromy action for bundles of punctured curves. As a by-product, we obtain a classification of all fix-point-free automorphisms on curves of genus at most [Formula: see text].

中文翻译：

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带有小签名的双小平纤维

Kodaira 纤维化是具有非等微纤维化的一般类型的表面，它们是可微分的纤维束。众所周知，它们具有可被 [公式：见正文] 整除的正签名。只有签名 16 及更多的示例才为人所知。我们回顾了构造允许两个独立纤维的低签名示例的方法。特别注意曲线乘积的分支覆盖，我们通过研究穿孔曲线束的单调作用来分析这些覆盖。作为一个副产品，我们最多可以得到一个属曲线上所有不定点自同构的分类[公式：见正文]。