Fine moduli space of rigid stable families to projective space
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In FP-notes. in Theorem 3, pages 16-17, in order to prove that a functor of rigid stable families (in genus zero) has fine moduli space, they defined a $H$-balanced morphism and they show that we have a morphism $ phi:B to overline{M} _{0,m}$ which is $H$-balanced, and every $H$-balanced morphism $varphi:X to overline{M}_{0,m}$ factor through $B$.
Now they consider in the paper locally free sheaves $pi_{B*}phi^*(H_i otimes H_0^{-1}) = G_i$ and consider total spaces of these sheaves, and finally consider a bundle associated with $G_i$ minus zero section by $Y_i$ then they consider $Y = Y_1 times... times Y_r$.
I want to know what was their motivation to consider $G_i$ and $Y=Y_1 times ...times Y_r $.
algebraic-geometry moduli-space
asked yesterday
Jigar Famil
62
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up vote
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In FP-notes. in Theorem 3, pages 16-17, in order to prove that a functor of rigid stable families (in genus zero) has fine moduli space, they defined a $H$-balanced morphism and they show that we have a morphism $ phi:B to overline{M} _{0,m}$ which is $H$-balanced, and every $H$-balanced morphism $varphi:X to overline{M}_{0,m}$ factor through $B$.
Now they consider in the paper locally free sheaves $pi_{B*}phi^*(H_i otimes H_0^{-1}) = G_i$ and consider total spaces of these sheaves, and finally consider a bundle associated with $G_i$ minus zero section by $Y_i$ then they consider $Y = Y_1 times... times Y_r$.
I want to know what was their motivation to consider $G_i$ and $Y=Y_1 times ...times Y_r $.
algebraic-geometry moduli-space
asked yesterday
Jigar Famil
62
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In FP-notes. in Theorem 3, pages 16-17, in order to prove that a functor of rigid stable families (in genus zero) has fine moduli space, they defined a $H$-balanced morphism and they show that we have a morphism $ phi:B to overline{M} _{0,m}$ which is $H$-balanced, and every $H$-balanced morphism $varphi:X to overline{M}_{0,m}$ factor through $B$.
Now they consider in the paper locally free sheaves $pi_{B*}phi^*(H_i otimes H_0^{-1}) = G_i$ and consider total spaces of these sheaves, and finally consider a bundle associated with $G_i$ minus zero section by $Y_i$ then they consider $Y = Y_1 times... times Y_r$.
I want to know what was their motivation to consider $G_i$ and $Y=Y_1 times ...times Y_r $.
algebraic-geometry moduli-space
asked yesterday
Jigar Famil
62
In FP-notes. in Theorem 3, pages 16-17, in order to prove that a functor of rigid stable families (in genus zero) has fine moduli space, they defined a $H$-balanced morphism and they show that we have a morphism $ phi:B to overline{M} _{0,m}$ which is $H$-balanced, and every $H$-balanced morphism $varphi:X to overline{M}_{0,m}$ factor through $B$.
Now they consider in the paper locally free sheaves $pi_{B*}phi^*(H_i otimes H_0^{-1}) = G_i$ and consider total spaces of these sheaves, and finally consider a bundle associated with $G_i$ minus zero section by $Y_i$ then they consider $Y = Y_1 times... times Y_r$.
I want to know what was their motivation to consider $G_i$ and $Y=Y_1 times ...times Y_r $.
algebraic-geometry moduli-space
algebraic-geometry moduli-space
asked yesterday
Jigar Famil
62
asked yesterday
Jigar Famil
62
asked yesterday
Jigar Famil
62
asked yesterday
Jigar Famil
62
asked yesterday
Jigar Famil
62
62
add a comment |
add a comment |
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