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RESEARCH PRODUCT

Corrigendum: Unirationality of Hurwitz Spaces of Coverings of Degree ≤5

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We correct Proposition 3.12 and Lemma 3.13 of the paper published in Vol. 2013, No.13, pp.3006-3052. The corrections do not affect the other statements of the paper. In this note, we correct a flow in the statement of Proposition 3.12 of [1] which also leads to a modification in the statement of Lemma 3.13 of [1]. We recall that in this proposition one considers morphisms of schemes X ?→π Y ?→q S, where q is proper, flat, with equidimensional fibers of dimension n and π is finite, flat and surjective. Imposing certain conditions on the fibers it is claimed that the loci of s € S fulfilling these conditions are open subsets of S. A missing condition should be added and the correct version of Parts (g) and (h) of Proposition 3.12 should be as follows: (g) Ys has no embedded components and the discriminant scheme of π s : Xs → Ys is of pure codimension one and smooth; (h) Ys has no embedded components and the discriminant scheme of π s : Xs → Ys is of codimension one, irreducible and generically reduced.