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Positivität relativer kanonischer Bündel und Krümmung höherer direkter Bildgarben auf Familien von Calabi-Yau-Mannigfaltigkeiten
In dieser Arbeit werden geometrische Eigenschaften des Modulraums polarisierter Calabi-Yau-Mannigfaltigkeiten mittels Methoden der komplex-analytischen Differentialgeometrie untersucht. Dazu werden Familien polarisierter Calabi-Yau-Mannigfaltigkeiten betrachtet. Die Fasern einer solchen Familie besi...
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| フォーマット: | Dissertation |
| 言語: | ドイツ語 |
| 出版事項: |
Philipps-Universität Marburg
2015
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| オンライン･アクセス: | PDFフルテキスト |
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This thesis deals with geometric properties of the moduli space of polarized Calabi-Yau manifolds employing methods from complex-analytic differential geometry. Given a family of polarized Calabi-Yau manifolds, the fibers possess unique Ricci-flat Kähler metrics with cohomology classes prescribed by the polarization. These Kähler metrics induce a Hermitian metric on the relative canonical bundle of the family, whose curvature form is studied. Moreover, a sufficient condition for the existence of a semi-Ricci-flat Kähler metric on the total space of a family is shown. Furthermore, certain higher direct image sheaves, carrying natural Hermitian metrics which generalize the Weil-Petersson metric on the moduli space, are considered. The curvature tensor of these metrics is calculated and some applications are outlined.