We show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type with p g = 0 and K 2 = 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally we calculate the bicanonical degree of Kulikov surfaces, and prove that they verify the Bloch conjecture.
ErklärungIch versichere eidesstattlich, dass ich diese Arbeit selbständig verfasst habe, und ich keine anderen als die von mir angegebenen Quellen und Hilfsmittel benutzt habe.Ich bestätige, dass Hilfe von gewerblichen Promotionsberatern bzw. -vermittlern oderähnlichen Dienstleistern weder bisher in Anspruch genommen wurde noch künftig in Anspruch genommen wird.Ich bestätige, dass ich keine frühere Promotionsversuche gemacht habe. Unterschrift des Autors i AcknowledgementsIt is my pleasure to express here my gratitude to my supervisor Prof. Fabrizio Catanese for suggesting me this research problem and for his continual guidance, as well as sharing his point of view about Mathematics and a lot of his personal experience in life.My gratitude also goes to Prof. Ingrid Bauer for encouraging me to explore different fields of Mathematics. Moreover, her care to me during my sickness made me feel like home while I was staying in a country distant from mine.Many thanks to all current and former colleagues in the Lehrstuhl Mathematik VIII of Universität Bayreuth, in particular to Michael Lönne, Fabio Perroni, Masaaki Murakami, Stephen Coughlan, Matteo Penegini, Wenfei Liu and Yifan Chen, for their help on my thesis, inspiring discussions on Mathematical ideas, sharing about the cultures and lifestyles of their own countries, and, most importantly, their encouragements which helped me to get through the most depressing period of my Ph.D. study. Thanks also to our secretary Leni Rostock who helped to sort out all the troubles during my stay in Bayreuth, from getting the residence permit to finding a medical doctor. Thanks to her, we have never missed the birthday of anybody in Lehrstuhl VIII. Wish that she would enjoy her life after retirement.Special thanks to my M.Phil. supervisor Prof. Ngaiming Mok, who taught me the basics about the Bochner-Kodaira formulas; and to Michael Lönne, Florian Schrack, Sascha Weigl and Christian Gleißner who helped me to translate the abstract and summary into German.I would also like to thank DAAD for their support under the Forschungsstipendien für Doktoranden.Lastly, I would like to declare that I owe my friends outside the Mathematics community in both Hong Kong and Germany a lot. Without their comforts and encouragements, this thesis could never be finished. My debts to them can never be fully redeemed. I am also badly indebted to my parents, who have given me freedom to do whatever I wish.ii AbstractThe Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert-Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both line...
We show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type with p g = 0 and K 2 = 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally we calculate the bicanonical degree of Kulikov surfaces, and prove that they verify the Bloch conjecture.
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