The nonabelian Kodaira-Spencer map is explicitly the composition of the usual Kodaira-Spencer map of the family with a natural cohomology map induced by the universal Higgs field.
The associated map of the nonabelian gauss-manin connection.Central European Journal of Mathematics, 10:1–15, 05 2012
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Nonabelian Kodaira-Spencer maps
The nonabelian Kodaira-Spencer map is explicitly the composition of the usual Kodaira-Spencer map of the family with a natural cohomology map induced by the universal Higgs field.