We discuss the problem of enumerating rational surfaces in 3-dimensional projective
space, as an analogue of Gromov-Witten invariants. It leads naturally to moduli spaces
of cofigurations of $n$ marked points in projective planes. We discuss the "Chow
quotients" of Kapranov, and present a new version of this construction which gives a
smooth moduli space for configurations of 6 points. We conjecture that the same
construction yields a smoothing of the moduli space of configurations of any number of
points in the plane.
We also briefly present a formula for enumeration of surfaces with a singular line.
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