Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension.
- Resource Type
- Article
- Authors
- Cao, Junyan; Guenancia, Henri; Păun, Mihai
- Source
- Journal für die Reine und Angewandte Mathematik. Oct2021, Vol. 2021 Issue 779, p1-36. 36p.
- Subject
- *EINSTEIN manifolds
*COMMERCIAL space ventures
*LOGICAL prediction
- Language
- ISSN
- 0075-4102
Given a Kähler fiber space p : X → Y whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle KX/Y of p. We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension). [ABSTRACT FROM AUTHOR]