6533b826fe1ef96bd128443b

RESEARCH PRODUCT

Irreducibility of Hurwitz spaces of coverings of an elliptic curve of prime degree with one point of total ramification

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Let Y be an elliptic curve, p a prime number and WH_{p,n}(Y) the Hurwitz space that parametrizes equivalence classes of p-sheeted branched coverings of Y , with n branch points, n − 1 of which are points of simple ramification and one of total ramification.In this paper, we prove that WH_{p,n}(Y) is irreducible if n − 1≥ 2 p.