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 ) ⊗...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Revista matemática complutense 2023, Vol.36 (1), p.57-72
Hauptverfasser: Biswas, Indranil, Bottacin, Francesco, Gómez, Tomás L.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
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.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-021-00418-7