| Résume | Let X be a simply-connected compact Kähler (or complex projective) manifold with first Chern class equal to zero, and let L be a "semi positive" line bundle on X. The non-vanishing problem for K-trivial varieties asks if some multiple of L has a global section. This problem is very difficult and open even for Calabi-Yau threefolds. In this talk I will present joint work with Vlad Lazic and Christian Lehn where we exhibit some geometric obstructions for the existence of such a section and show non-vanishing results for varieties where the Euler characteristic does not vanish. |
