In [3] D. Eisenbud and J. Harris posed the following question: What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type? We answer their question for one-dimensional families of smooth curves degenerating to stable curves with just two components meeting at points in general position. In this note we treat only those families whose total ...

Let π : X −→ Y be a good quotient of a smooth variety X by a reductive algebraic group G and 1 ≤ k ≤ dim (Y ) an integer. We prove that if, locally, any invariant horizontal differential k-form onX (resp. any regular differential k-form on Y ) is a Kähler differential form on Y then codim (Ysing) > k + 1. We also prove that the dualizing sheaf on Y is the sheaf of invariant horizontal dim (Y )-...