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Higgs-Demailly System and Positivity of Higgs Bundles
We prove that the Higgs-Demailly system on a compact Riemann surface admits a smooth admissible solution at its terminal parameter if and only if the Higgs bundle is H-ample. This gives an independent analytic characterization of H-ampleness by Griffiths-positive Hitchin-Simpson curvature. The proof
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