Cohomology of graph hypersurfaces associated to certain Feynman graphs [Elektronische Ressource] / von Dzmitry Doryn

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Cohomology of graphhypersurfaces associated tocertain Feynman graphsDissertationzur Erlangung des GradesDoktor der Naturwissenschaften(Dr.rer.nat.)vorgelegt beimFachbereich Mathematikder Universit˜at Duisburg-Essenvon Dzmitry Dorynaus Vitsebsk, Wei…russlandTag der Disputation 2. Dezember 2008Vorsitzender der Prufungsk˜ ommission Prof. Dr. Markus KunzeErster Gutachter Prof. Dr. H¶elµene EsnaultZweiter Gutachter Prof. Dr. Eckart Viehweg2AcknowledgmentsI would like to thank Prof.Dr.H¶elµene Esnault and Prof.Dr.Eckart Viehwegfor the possibility to come to Germany, to join their research group and tostudy algebraic geometry.I am very grateful to my advisor Prof.Dr. H¶elµene Esnault for her constantsupport and guidance throughout the preparation of this thesis.I would like to thank Dr. Kay Rulling˜ for reading this thesis and for help.I also want to thank Dr. Georg Hein for useful comments.Finally, I want to thank all my colleagues at the university of Essen for thenice friendly atmosphere during this three wonderful years.34ContentsIntroduction 71 Preliminaries 91.1 Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Graph polynomials . . . . . . . . . . . . . . . . . . . . . . . 181.3 Cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 GZZ 332.1 ZZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3352.2 Generalized zigzag graphs . . . . . . . . . . . . . . . . . . . 462.

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• Mathematics

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• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2009
• Nombre de lectures: 41
• Langue: English

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