Comparison of Poisson structures on moduli spaces
Let X be a complex irreducible smooth projective curve, and let L be an algebraic line bundle on X with a nonzero section σ 0 . Let M denote the moduli space of stable Hitchin pairs ( E , θ ) , where E is an algebraic vector bundle on X of fixed rank r and degree δ , and θ ∈ H 0 ( X , E n d ( E ) ⊗...
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Veröffentlicht in: | Revista matemática complutense 2023, Vol.36 (1), p.57-72 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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Zusammenfassung: | Let
X
be a complex irreducible smooth projective curve, and let
L
be an algebraic line bundle on
X
with a nonzero section
σ
0
. Let
M
denote the moduli space of stable Hitchin pairs
(
E
,
θ
)
, where
E
is an algebraic vector bundle on
X
of fixed rank
r
and degree
δ
, and
θ
∈
H
0
(
X
,
E
n
d
(
E
)
⊗
K
X
⊗
L
)
. Associating to every stable Hitchin pair its spectral data, an isomorphism of
M
with a moduli space
P
of stable sheaves of pure dimension one on the total space of
K
X
⊗
L
is obtained. Both the moduli spaces
P
and
M
are equipped with algebraic Poisson structures, which are constructed using
σ
0
. Here we prove that the above isomorphism between
P
and
M
preserves the Poisson structures. |
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ISSN: | 1139-1138 1988-2807 |
DOI: | 10.1007/s13163-021-00418-7 |