The Effective Cone of the Kontsevich Moduli Space

Coskun, Izzet ; Harris, Joe ; Starr, Jason

Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 519-534

Résumé

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

Détail

DOI : 10.4153/CMB-2008-052-5

Mots-clés : 14D20, 14E99, 14H10

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