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The isomonodromic tau function of the Fuchsian differential equationsassociated to Frobenius structures on Hurwitz spaces can be viewed as a sectionof a line bundle on the space of admissible covers. We study the asymptoticbehavior of the tau function near the boundary of this space and compute itsdivisor. This yields an explicit formula for the pullback of the Hodge class tothe space of admissible covers in terms of the classes of compactificationdivisors.

Isomonodromic tau function on the space of admissible covers