On a stratification of the Kontsevich space of the Grassmannian G(2,4) and enumerative geometry

Details On a stratification of the Kontsevich space of the Grassmannian G(2,4) and enumerative geometry On a stratification of the Kontsevich space of the Grassmannian G(2,4) and enumerative geometry

2006-06-27

arxiv.org/abs/math/0606673v3

Journal of Pure and Applied Algebra, 213 (2009) 857-868

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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 $\mathbb{P}^{3}$ with a minimal directrix of degree 2.

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