Geodesic
The Ample Cone of the Kontsevich Moduli Space
Canadian journal of mathematics, Tome 61 (2009) no. 1, pp. 109-123

Voir la notice de l'article provenant de la source Cambridge University Press

We produce ample (resp. NEF, eventually free) divisors in the Kontsevich space ${{\overline{\mathcal{M}}}_{\text{0,}n}}\left( {{\mathbb{P}}^{r}},d \right)$ of $n$ -pointed, genus 0, stable maps to ${{\mathbb{P}}^{r}}$ , given such divisors in ${{\overline{\mathcal{M}}}_{\text{0,}n+d}}$ We prove that this produces all ample (resp. NEF, eventually free) divisors in ${{\overline{\mathcal{M}}}_{\text{0,}n}}\left( {{\mathbb{P}}^{r}},\,d \right)$ As a consequence, we construct a contraction of the boundary $\,\,\mathop{\bigcup }_{k=1}^{\left\lfloor {d}/{2}\; \right\rfloor }\,{{\Delta }_{k,d-k}}$ in ${{\overline{\mathcal{M}}}_{\text{0,}0}}\left( {{\mathbb{P}}^{r}},d \right)$ analogous to a contraction of the boundary $\mathop{\bigcup }_{k=3}^{\left\lfloor {n}/{2}\; \right\rfloor }\,{{\widetilde{\Delta }}_{k,n-k}}$ in ${{\overline{\mathcal{M}}}_{\text{0,}n}}$ first constructed by Keel and McKernan. 
Coskun, Izzet; Harris, Joe; Starr, Jason. The Ample Cone of the Kontsevich Moduli Space. Canadian journal of mathematics, Tome 61 (2009) no. 1, pp. 109-123. doi: 10.4153/CJM-2009-005-8
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