Discrete Symmetries of Calabi-Yau Hypersurfaces in Toric Four-Folds

Understand

We analyze freely-acting discrete symmetries of Calabi-Yau three-folds defined as hypersurfaces in ambient toric four-folds.

• An algorithm which allows the systematic classification of such symmetries which are linearly realised on the toric ambient space is devised.
• This algorithm is applied to all Calabi-Yau manifolds with $h^{1,1}(X)\leq 3$ obtained by triangulation from the Kreuzer-Skarke list, a list of some $350$ manifolds.
• All previously known freely-acting symmetries on these manifolds are correctly reproduced and we find five manifolds with freely-acting symmetries.