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• W4207071124 abstract "Abstract Let X be a complex irreducible smooth projective curve, and let $${{mathbb {L}}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>L</mml:mi> </mml:math> be an algebraic line bundle on X with a nonzero section $$sigma _0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . Let $${mathcal {M}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>M</mml:mi> </mml:math> denote the moduli space of stable Hitchin pairs $$(E,, theta )$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>E</mml:mi> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>θ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where E is an algebraic vector bundle on X of fixed rank r and degree $$delta $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>δ</mml:mi> </mml:math> , and $$theta , in , H^0(X,, {mathcal {E}nd}(E)otimes K_Xotimes {{mathbb {L}}})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mspace /> <mml:mo>∈</mml:mo> <mml:mspace /> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>⊗</mml:mo> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:mo>⊗</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . Associating to every stable Hitchin pair its spectral data, an isomorphism of $${mathcal {M}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>M</mml:mi> </mml:math> with a moduli space $${mathcal {P}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>P</mml:mi> </mml:math> of stable sheaves of pure dimension one on the total space of $$K_Xotimes {{mathbb {L}}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:mo>⊗</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> is obtained. Both the moduli spaces $${mathcal {P}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>P</mml:mi> </mml:math> and $${mathcal {M}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>M</mml:mi> </mml:math> are equipped with algebraic Poisson structures, which are constructed using $$sigma _0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . Here we prove that the above isomorphism between $${mathcal {P}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>P</mml:mi> </mml:math> and $${mathcal {M}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>M</mml:mi> </mml:math> preserves the Poisson structures." @default.
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• W4207071124 date "2021-12-28" @default.
• W4207071124 modified "2023-10-14" @default.
• W4207071124 title "Comparison of Poisson structures on moduli spaces" @default.
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