Geodesic
The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class
Forum of Mathematics, Sigma, Tome 9 (2021)

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Let X be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that X admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth. We then prove that this unobstructedness assumption holds in at least three cases: if X has toroidal singularities, if X has finite quotient singularities and if the cohomology group ${\mathrm {H}^{2} \!\left ( X, {\mathscr {T}_{X}} \right )}$ vanishes. 
@article{10_1017_fms_2021_18,
     author = {Patrick Graf and Martin Schwald},
     title = {The {Kodaira} {Problem} for {K\"ahler} {Spaces} with {Vanishing} {First} {Chern} {Class}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2021.18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.18/}
}
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Patrick Graf; Martin Schwald. The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.18

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