Seshadri constants and geometry of surfaces [Elektronische Ressource] / von Wioletta Syzdek

Seshadri constantsand geometry of surfacesDissertationzur Erlangung des GradesDoktor der Naturwissenschaften(Dr. rer. nat.)vorgelegt beimFachbereich Mathematik und Informatikder Universit¨at Duisburg-Essenvon Wioletta Syzdekaus My´sleniceTag der Disputation 20. Juli 2005Vorsitzender der Prufungsk¨ ommission Prof. Dr. Karl-Josef WitschErster Gutachter Prof. Dr. Tomasz SzembergZweiter Gutachter Prof. Dr. Eckart ViehwegAcknowledgmentsI am very grateful to Tomasz Szemberg for his invaluable support and theguidance throughout the preparation of this thesis.IwanttothankmyformerteacherHalszkaTutaj-Gasinsk´ aforthepossibilityofbeginningofmyPhDstudiesandforlettingmeknowtheideaofsymplecticpacking.I would like to thank H´el`ene Esnault and Eckart Viehweg for making mystudy in Essen possible, for help with bureaucracy - in particular withAusl¨anderamt in Essen.I want to thank my colleagues: Kay Rulling¨ , Stefan Kukulies and AndreChatzistamatiou for friendly atmosphere in the office and help during mystudy here.Finally I would like to thank my parents, my grandmother and my brotherfor support in difficult times.Contents1 Introduction 12 Seshadri constants and the Nagata-Biran conjecture. 32.1 Seshadri constants - basics definitions and properties. . . . . . 32.2 Multiple points Seshadri constants and the Nagata-Biran con-jecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Seshadri constants on ruled surfaces. 93.