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arXiv · 2001.06339

The Kodaira problem for K\"ahler spaces with vanishing first Chern class

Patrick Graf·Martin Schwald
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Abstract

Let $X$ be a normal compact K\"ahler 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.

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Patrick Graf, Martin Schwald. 2020-01-17. The Kodaira problem for K\"ahler spaces with vanishing first Chern class. https://doi.org/10.1017/fms.2021.18

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