Proves equivalence between holomorphicity of isomonodromic Higgs bundle families and isomonodromicity under C*-rescaling, yielding a local characterization of non-abelian Noether-Lefschetz loci.
arXiv preprint arXiv:2512.07152 , year=
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The non-abelian Noether-Lefschetz locus coincides with the locus of holomorphicity of the isomonodromic deformation of Higgs bundles, characterized locally by vanishing of obstruction classes in the differential graded Lie algebra of the deformation.
Infinitesimal rigidity is established for irreducible cyclic surfaces and n-alternating surfaces in H^{p,q}, unifying prior results on maximal space-like surfaces, alternating holomorphic curves, and A-surfaces.
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Isomonodromic deformations, $\mathbb C^*$-actions, and characterization of non-abelian Noether-Lefschetz loci on Dolbeault moduli spaces
Proves equivalence between holomorphicity of isomonodromic Higgs bundle families and isomonodromicity under C*-rescaling, yielding a local characterization of non-abelian Noether-Lefschetz loci.
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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 coincides with the locus of holomorphicity of the isomonodromic deformation of Higgs bundles, characterized locally by vanishing of obstruction classes in the differential graded Lie algebra of the deformation.
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Infinitesimal Rigidity of Cyclic Surfaces and Alternating Surfaces
Infinitesimal rigidity is established for irreducible cyclic surfaces and n-alternating surfaces in H^{p,q}, unifying prior results on maximal space-like surfaces, alternating holomorphic curves, and A-surfaces.