The non-abelian Noether-Lefschetz locus equals the maximal complex analytic subvariety on which the isomonodromic deformation of Higgs bundles is holomorphic.
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Certain degeneration limits of Calabi-Yau and hyperkähler manifolds with bounded periods remain Kähler, giving new proofs and complete solutions to the Soldatenkov-Verbitsky and Perego conjectures.
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Higher order isomonodromic deformation of Higgs bundles and a characterization of the non-abelian Noether-Lefschetz locus
The non-abelian Noether-Lefschetz locus equals the maximal complex analytic subvariety on which the isomonodromic deformation of Higgs bundles is holomorphic.
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Degenerations and Stability of K\"ahler Structures on Calabi--Yau Manifolds
Certain degeneration limits of Calabi-Yau and hyperkähler manifolds with bounded periods remain Kähler, giving new proofs and complete solutions to the Soldatenkov-Verbitsky and Perego conjectures.