In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, $\Kgnb{0,0}(\PP^r,d)$, stabilize when $r \geq d$. We give a complete characterization of the effective divisors on $\Kgnb{0,0}(\PP^d,d)$. They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.

MSC Classifications:

14D20, 14E99, 14H10 show english descriptions Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
None of the above, but in this section
Families, moduli (algebraic) 14D20 - Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
14E99 - None of the above, but in this section
14H10 - Families, moduli (algebraic)

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