Symplectic Geometry of Higgs Moduli and the Hilbert Scheme of Points

2025/05/05 by Jia, Zelin · 1 citation
#14H60 #14J42 #53D30 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2505.02334

Abstract

We show that the isomorphism between the moduli space of certain parabolic Higgs bundles over an elliptic curve and the Hilbert scheme of n points of the cotangent bundle of the elliptic curve is a symplectomorphism with respect to their natural symplectic structures.

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• From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes

Related

• Hilbert schemes as moduli of Higgs bundles and local systems
• Symplectic resolutions for Higgs moduli spaces
• Symplectic resolutions of moduli spaces of G-Higgs bundles
• Moduli spaces of parabolic U(p,q)-Higgs bundles
• Torelli theorem for the moduli space of symplectic parabolic Higgs\n bundles