  We show that the water waves system is locally wellposed in weighted Sobolev
spaces which allow for interfaces with corners. No symmetry assumptions are
required. These singular points are not rigid: if the initial interface
exhibits a corner, it remains a corner but generically its angle changes. Using
a characterization of the asymptotic behavior of the fluid near a corner that
follows from our a priori energy estimates, we show the existence of initial
data in these spaces for which the fluid becomes singular in finite time.
