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The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class

Published online by Cambridge University Press:  15 March 2021

Patrick Graf
Lehrstuhl für Mathematik I, Universität Bayreuth, 95440Bayreuth, Germany; E-mail: URL:
Martin Schwald
Fakultät für Mathematik, Universität Duisburg–Essen, 45117Essen, Germany; E-mail: URL:


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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.

Algebraic and Complex Geometry
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© The Author(s), 2021. Published by Cambridge University Press


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