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arXiv · 1911.00798

Non-algebraic deformations of flat K\"ahler manifolds

Vasily Rogov
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Abstract

Let $X$ be a compact K\"ahler 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 $H^0(X, \Omega^2) \neq 0$. 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 K\"ahler manifolds with vanishing first Betti number.

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Vasily Rogov. 2019-11-02. Non-algebraic deformations of flat K\"ahler manifolds. https://arxiv.org/abs/1911.00798

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