Abstract
Let
C
be a smooth projective irreducible curve of genus
g
. And let
G
α
(n,d,l)
be the moduli space of
α
stable pairs of a vector bundle of $\rank n, °d$ and a subspace of
H
0
(C,E)
of
dim=l
. We find an explicit birational map from
G
α
(n,d,n+1)
to
G
α
(1,d,n+1)
for
C
general,
1/α≫0
and
g≥
n
2
−1
. Because of this and other examples, we conjecture
G
α
(a,d,a+z)
maps birationally to
G
α
(z,d,a+z)
for
1/α≫0
and
C
general with
g>2
.