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We focus on the positive dimensional fibres of the Prym map$\mathcal{P}_{g,r}$. We present a direct procedure to investigate infinitelymany examples of positive dimensional fibres. Such procedure uses families ofGalois coverings of the line admitting a 2-sheeted Galois intermediatequotient. Then we generalize to families of Galois coverings of the lineadmitting a Galois intermediate quotient of higher degree and we show that thehigher degree analogue of the aforementioned procedure gives all the knowncounterexamples to a conjecture by Xiao on the relative irregularity of afibration.

Explicit analysis of positive dimensional fibres of $ \mathcal{P}_{g,r} $ and Xiao conjecture