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arXiv 2001.063392020-01math.AGmath.CVmath.DG

The Kodaira problem for Kähler spaces with vanishing first Chern class

Patrick Graf, Martin Schwald

备注：: Final version, to appear in Forum of Mathematics, Sigma
发表信息：: Forum of Mathematics, Sigma 9 (2021) e24
DOI：: 10.1017/fms.2021.18

英文摘要：

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.

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