On a stratification of the Kontsevich space of the Grassmannian G(2,4) and enumerative geometry
arXiv:math/0606673
Abstract
We study the geometry of the Kontsevich compactification of stable maps to the Grassmannian of lines in the projective space. We consider a stratification of this space. As an application we compute the degree of the variety parametrizing rational ruled surfaces with a minimal directix of degree d/2-1 by intersecting divisors in the moduli space of stable maps. For example, there are 128054031872040 rational ruled sextics passing through 25 points in with a minimal directrix of degree 2.
17 pages