Galois closure of a 5-fold covering and decomposition of its Jacobian

Abstract: For an arbitrary 5-fold ramified covering between compact Riemann surfaces, every possible Galois closure is determined in terms of the ramification data of the map; namely, the ramification divisor of the covering map. Since the group that acts on the Galois closure also acts on the Jacobian variety of the covering surface, we describe its group algebra decomposition in terms of the Jacobian and Prym varieties of the intermediate coverings of the Galois closure. The dimension and induced polarization of each abelian variety in the decomposition is computed in terms of the ramification data of the covering map.