
The Ample Cone of the Kontsevich Moduli Space
We produce ample (resp.\ NEF, eventually free) divisors in the
Kontsevich space $\Kgnb{0,n} (\mathbb P^r, d)$ of $n$pointed,
genus $0$, stable maps to $\mathbb P^r$, given such divisors in
$\Kgnb{0,n+d}$. We prove that this produces all ample (resp.\ NEF,
eventually free) divisors in $\Kgnb{0,n}(\mathbb P^r,d)$.
As a consequence, we construct a contraction of the boundary
$\bigcup_{k=1}^{\lfloor d/2 \rfloor} \Delta_{k,dk}$ in
$\Kgnb{0,0}(\mathbb P^r,d)$, analogous to a contraction of
the boundary $\bigcup_{k=3}^{\lfloor n/2 \rfloor}
\tilde{\Delta}_{k,nk}$ in $\kgnb{0,n}$ first constructed by Keel
and McKernan.
Categories:14D20, 14E99, 14H10 