The liftability of elliptic surfaces [Elektronische Ressource] / vorgelegt von Holger Partsch

The Liftability of Elliptic SurfacesInaugural-Dissertationzur Erlangung des Doktorgradesder Mathematisch-Naturwissenschaftlichen Fakult¨atder Heinrich-Heine-Universit¨at Du¨sseldorfvorgelegt vonHolger Partschaus AugsburgDu¨sseldorf, Dezember 2010Aus dem Mathematischen Institutder Heinrich-Heine-Universit¨at Dus¨ seldorfGedruckt mit der Genehmigung derMathematisch-Naturwissenschaftlichen Fakult¨at derHeinrich-Heine-Universit¨at Dus¨ seldorfReferent: Prof. Dr. Stefan Schr¨oerKoreferent: Dr. habil. Cristiana BertolinTag der mundlic¨ hen Pruf¨ ung: 21.01.2011Erstellungsdatum der elektronischen Version: 25.01.2011ContentsAcknowledgments vZusammenfassung viiSummary ixIntroduction xiBackground and motivation xivNotations and conventions xviChapter 1. Smooth elliptic fibrations and elliptic fibre bundles 11. Preliminaries: Deformation theory and thickened schemes 12. Elliptic fibre bundles: Definition and examples 33. Elliptic curves and their moduli 44. Deformations of Jacobian elliptic fibre bundles 55. Non-liftable elliptic fibre bundles 86. Deformations of elliptic torsors 97. Elliptic fibre bundles of Kodaira dimension one 128. Bielliptic surfaces 15Chapter 2. Liftings of semistable elliptic fibrations 271. Semistable genus-1 curves and generalized elliptic curves 272. Modular invariants and isomorphism types over complete bases 293. Moduli of generalized elliptic curves with level structures 314. Level structures and liftability 325.