Jimmy Dillies

Generalized Borcea-Voisin Construction


We generalize the construction of Borcea and Voisin of Calabi-Yau threefolds by allowing automorphisms of higher order and considering both three- and fourfolds. We classify all orbifolds / varieties obtained in this way and show that they come in mirror pairs only if constructed through involutions. We gave suggestions on the obstruction to the existence of 'classical' mirrors.