Cyclic coverings, Calabi-Yau manifolds and complex multiplication [Elektronische Ressource] / von Jan Christian Rohde

Cyclic coverings, Calabi-Yau manifoldsand Complex multiplicationDissertation zur Erlangung des GradesDoktor der Naturwissenschaften(Dr. rer. nat.)vorgelegt beimFachbereich Mathematikder Universit¨at Duisburg-EssenvonJan Christian Rohdegeboren inGelsenkirchenErster Gutachter: Prof. Dr. Eckart ViehwegZweiter Gutachter: Priv.-Doz. Dr. Martin Mo¨llerDatum der mun¨ dlichen Prufung¨ : 14. Dezember 20072AcknowledgmentsI am very grateful to Eckart Viehweg for giving me the subject of this thesis and hisexcellent guidance and support, not only during the work on this topic, but from thebeginning of my mathemathical studies.Moreover, I would like to thank especially Martin M¨oller for many fruitful and stimu-lating hints and discussions, and for reading this thesis and pointing out several mistakes.I want to thank Kang Zuo and Stefan Muller-Sta¨ ch for the hint to the essay [48] ofC. Voisin, which provided the main idea of the construction of many examples ofCMCYfamilies of 3-manifolds and finally of the construction of the Borcea-Voisin tower.Many thanks to Ulrich G¨ortz for his instructive course about Shimura varieties atMainz and to Gebhard B¨ockle for his interesting reading course about Shimura curves.Moreover, I would like to thank Bernd Siebert and Claire Voisin for stimulating dis-cussions about maximality and the Voisin mirror families.