We prove deformation obstructions concentrate on isolated singularities in compact Kähler spaces, implying unobstructed locally trivial deformations.
Let X be a compact normal Kähler space whose canonical sheaf is a rank-one free OX module and whose singularities are isolated, rational and quasi-homogeneous. We prove then that under a topological hypothesis the obstruction to deforming X concentrates upon its singularities, generalizing partially the results of Namikawa--Gross. We prove also that under a certain hypothesis the locally trivial deformations of X are unobstructed.
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Yohsuke Imagi (2025) studied this question.
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