Veronese surfaces and line arrangements
Tom Graber and Kristian Ranestad
We formulate a generalization of Castelnuovo`s lemma on rational normal curves to d-uple Veronese surfaces and apply it to define a Hilbert scheme compactification of line arrangements in the Hilbert scheme of Veronese surfaces. In the case of arrangements of five lines, we find the compactification to be isomorphic to a Del Pezzo surface of degree 5. We thus recover previous results of Kapranov and Hacking.