All Questions

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 projective) ...

I am interested in a simply-connected compact complex manifold $M$ of dimension three with trivial canonical class. Note that if it is K"ahler, then it is a Calabi-Yau threefold. Its independent ...

I heard from string theorists thinking of the so-called "(1/2) K3 surface" or "half-K3 surface" as follows: Let $T^2 \times S^1$ be a 3-torus with spin structure periodic in all directions. $T^2 \...

Is something known about the higher homotopy groups of Calabi-Yau threefolds? For example, one of the easiest CYs is the quintic, defined as the anticanonical divisor in $\mathbb{CP}_4$. What are its ...

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