Lp Metric Geometry of Big and Nef Cohomology Classes

Let ( X , ω ) be a compact Kähler manifold of dimension n , and let θ be a closed smooth real (1,1)-form representing a big and nef cohomology class. We introduce a metric d p , p ≥ 1, on the finite energy space E p ( X , θ ) , making it a complete geodesic metric space.

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Bibliographic Details
Published in:Acta mathematica vietnamica 2020-03, Vol.45 (1), p.53-69
Main Authors: Di Nezza, Eleonora, Lu, Chinh H.
Format: Article
Language:English
Subjects:
Geometry
Homology
Mathematics
Mathematics and Statistics
Metric space
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Summary:Let ( X , ω ) be a compact Kähler manifold of dimension n , and let θ be a closed smooth real (1,1)-form representing a big and nef cohomology class. We introduce a metric d p , p ≥ 1, on the finite energy space E p ( X , θ ) , making it a complete geodesic metric space.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-019-00343-4