The Kodaira problem for K\"ahler spaces with vanishing first Chern class
Algebraic Geometry
2021-07-01 v2 Complex Variables
Differential Geometry
Abstract
Let be a normal compact K\"ahler space with klt singularities and torsion canonical bundle. We show that 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 has toroidal singularities, if has finite quotient singularities, and if the second cohomology group of its tangent sheaf vanishes.
Cite
@article{arxiv.2001.06339,
title = {The Kodaira problem for K\"ahler spaces with vanishing first Chern class},
author = {Patrick Graf and Martin Schwald},
journal= {arXiv preprint arXiv:2001.06339},
year = {2021}
}
Comments
Final version, to appear in Forum of Mathematics, Sigma