| We revisit the problem of extending the Prym map to the compactification of the moduli space of etale double covers of curves. It was shown by Friedman and Smith that the Prym map does not extend to a morphism, and the indeterminacy locus of the map to the second Voronoi toroidal compactification of the moduli space of abelian varieties was determined by Alexeev, Birkenhake, Hulek, and Vologodsky. We give a streamlined approach to this result, and the recent extension results for the Torelli map of Alexeev and Brunyate, and also study the indeterminacy locus of the Prym map to other toroidal compactifications. Joint work with S. Casalaina-Martin, K. Hulek, R. Laza. |