Deformation of Kähler manifolds

Junyan Cao (1)

1 IF - Institut Fourier

It has been shown by Claire Voisin in 2003 that one cannot always deform a compact Kähler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an additional semipositivity or seminegativity condition on the canonical bundle, the answer becomes positive, namely such a compact Kähler manifold can be approximated by deformations of projective manifolds.

Mots clés: Kähler manifolds; deformation; nef tangent bundle; semipositive anticanonical bundle; Kodaira conjecture

Domaines: Géométrie algébrique [math.AG]

Junyan Cao. Deformation of Kähler manifolds. 2013. ⟨hal-00749923v2⟩