VERONESE SURFACES AND LINE ARRANGEMENTS

TOM GRABER KRISTIAN RANESTAD

Abstract. 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.