Affiliation:
1. Dipartimento di Matematica, Università degli Studi di Trento , Via Sommarive 14, 38123 Trento , Italy
Abstract
Abstract
The moduli space
M
¯
0,
n
(
ℙ
1
,
1
)
${{\bar{M}}_{0,n}}\left( {{\mathbb{P}}^{1}},1 \right)$
of n-pointed stable maps is a Mori dream space whenever the moduli space
M
¯
0
,
n
+
3
of
(
n
+
3
)
${{\bar{M}}_{0,n+3}}\; \text{of} \;(n+3)$
pointed rational curves is, and
M
¯
0
,
n
(
ℙ
1
,
1
)
${{\bar{M}}_{0,n}}\left( {{\mathbb{P}}^{1}},1 \right)$
is a log Fano variety for n ≤ 5.