Calabi-Yau metrics on canonical bundles of complex flag manifolds

In the present paper we provide a description of complete Calabi-Yau metrics on the canonical bundle of generalized complex flag manifolds. By means of Lie theory we give an explicit description of complete Ricci-flat Kähler metrics obtained through the Calabi Ansatz technique. We use this approach...

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Bibliographic Details
Published in:Journal of algebra 2019-06, Vol.527, p.109-135
Main Authors: Correa, Eder M., Grama, Lino
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calabi-Yau varieties
Canonical bundles
Flag varieties
Lie Theory
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Summary:In the present paper we provide a description of complete Calabi-Yau metrics on the canonical bundle of generalized complex flag manifolds. By means of Lie theory we give an explicit description of complete Ricci-flat Kähler metrics obtained through the Calabi Ansatz technique. We use this approach to provide several explicit examples of noncompact complete Calabi-Yau manifolds, these examples include canonical bundles of non-toric flag manifolds (e.g. Grassmann manifolds and full flag manifolds).
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2019.02.027