The Kodaira problem for Kähler spaces with vanishing first Chern class

Abstract

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 second cohomology group of its tangent sheaf vanishes.

Final version, to appear in Forum of Mathematics, Sigma

References in corpus (3)

• The global moduli theory of symplectic varieties
• Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
• Orbifoldes à premi\ere classe de Chern nulle