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.

中文翻译：

---

第一陈类消失的 Kähler 空间的小平问题

让X是具有 klt 奇点和扭转规范丛的正规紧致 Kähler 空间。我们表明X如果它的局部平凡变形空间是光滑的，则允许任意小的变形是射影变体. 然后，我们证明这种通畅性假设至少在三种情况下成立：如果X有环形奇点，如果X具有有限商奇点并且如果上同调群 ${\mathrm {H}^{2} \!\left ( X, {\mathscr {T}_{X}} \right )}$ 消失。