turkmath.org

In this talk I will present a class of non-simply connected Calabi-Yau 3-folds with positive Euler characteristic which are the quotient spaces of fixed-point-free group actions on desingularizations of singular Schoen 3-folds. A Schoen 3-fold is the fiber product of two rational elliptic surfaces with section. Smooth Schoen 3-folds are simply connected CY 3-folds. Desingularizations of certain singular Schoen 3-folds by small resolutions have the same property. If a finite group G acts freely on such a 3-fold, the quotient is again a CY 3-fold. I will present how to classify such group actions using the automorphism groups of rational elliptic surfaces with section. The smooth Schoen 3-fold case gives 0 Euler characteristic whereas the singular case results in positive Euler characteristic for the quotient CY threefolds.