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Non-algebraic deformations of flat Kähler manifolds
Rogov V.
Let X be a compact Kähler manifold with vanishing Riemann curvature. We prove that there exists a manifold X′, deformation equivalent to X, which is not an analytification of any projective variety, if and only if H^0(X, Ω^2)≠0. Using this, we recover a recent theorem of Catanese and Demleitner, which states that a rigid smooth quotient of a complex torus is always projective. We also produce many examples of non-algebraic flat Kähler manifolds with vanishing first Betti number.
Research target:
Mathematics
Language:
English
Publication based on the results of:
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Springer, 2027.
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