Compact Kähler manifolds with no projective specialization

Date: 2021-11-18

Time: 11:00 - 12:00

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Claire Voisin


We show the existence of a compact Kähler manifold which does not fit in a proper flat family over an irreducible base with one projective (possibly singular) fiber. This strengthens our earlier counterexamples to the Kodaira algebraic approximation problem, where we considered only smooth families. Our main tool is the limit Hodge structure on cohomology as constructed by Steenbrink, which allows to study the singular fibers.