Item type:Thesis, Open Access

Positivität relativer kanonischer Bündel und Krümmung höherer direkter Bildgarben auf Familien von Calabi-Yau-Mannigfaltigkeiten

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Date

2015-12-16

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Philipps-Universität Marburg
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Abstract

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.

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Dates
Created: 2015Issued: 2015-12-16
DOI
https://doi.org/10.17192/z2015.0401
Faculty
Fachbereich Mathematik und Informatik
Publisher
Philipps-Universität Marburg
Language
ger
Data types
DoctoralThesis
Keywords
Positivity of relative canonical bundlesCalabi-Yau manifoldPositivität relativer kanonischer BündelKrümmung höherer direkter BildgarbenSemi-Ricci-flat metricsCurvature of higher direct image sheavesSemi-Ricci-flache MetrikenModuli space
DFG-subjects
ModulraumCalabi-Yau-MannigfaltigkeitWeil-Petersson-Metrik
DDC-Numbers
510
License
https://rightsstatements.org/vocab/InC-NC/1.0/
URI
https://open.uni-marburg.de/handle/10.17192/z2015.0401
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Braun, Matthias: Positivität relativer kanonischer Bündel und Krümmung höherer direkter Bildgarben auf Familien von Calabi-Yau-Mannigfaltigkeiten. : Philipps-Universität Marburg 2015-12-16. DOI: https://doi.org/10.17192/z2015.0401.

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This item has been published with the following license: In Copyright