16
votes
2answers
579 views

Moishezon manifolds with vanishing first Chern class

Suppose $M$ is a Moishezon manifold with $c_1(M)=0$ in $H^2(M,\mathbb{R})$. Does it follow that $K_M$ is torsion in $\mathrm{Pic}(M)$? This is true whenever $M$ is Kähler (and therefore ...
3
votes
1answer
554 views

Are there any symplectic but not holomorphic Calabi-Yau manifolds in real dimensions 4 and 6?

Are there any symplectic but not complex Calabi- Yau manifolds in real dimensions 4 and 6?