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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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.
For families of curves of genus at least 1 the Gauss-Manin connections are isomorphic to the group cohomology of the geometric relative fundamental group, yielding a cohomological interpretation and a de Rham K(π,1) surface after shrinking.
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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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Tannakian duality and Gauss-Manin connections for a family of curves
For families of curves of genus at least 1 the Gauss-Manin connections are isomorphic to the group cohomology of the geometric relative fundamental group, yielding a cohomological interpretation and a de Rham K(π,1) surface after shrinking.