Calabi-Yau-threefolds with Picard number rho(X)=2 and their Kahler cone I

摘要

We describe properties of the Kahler cone of general Calabi-Yau-three-folds with Picard number rho(X) = 2 and prove the rationality of the Kahler cone, if X is a Calabi-Yau-hypersurface in a P-2-bundle over P-2 and c(3)(X) less than or equal to -54. Without the latter assumption we prove the positivity of c(2)(X). [References: 9]