Advanced Studies in Pure Mathematics

Relative adjoint transcendental classes and Albanese map of compact Kähler manifolds with nef Ricci curvature

Mihai Păun

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Abstract

We establish here the surjectivity of the Albanese map corresponding to compact Kähler manifold whose anti-canonical bundle is nef. This answers a question raised by J.-P. Demailly, Th. Peternell and M. Schneider. One of the main techniques we are using is the positivity of the relative canonical bundle associated to Kähler fiber spaces, obtained via the “psh variation” of fiber-wise twisted Kähler-Einstein metrics.

Article information

Source
Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, K. Oguiso, C. Birkar, S. Ishii and S. Takayama, eds. (Tokyo: Mathematical Society of Japan, 2017), 335-356

Dates
Received: 26 October 2013
First available in Project Euclid: 23 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540319496

Digital Object Identifier
doi:10.2969/aspm/07410335

Zentralblatt MATH identifier
1392.32010

Subjects
Primary: 32Gxx: Deformations of analytic structures 14Dxx: Families, fibrations

Keywords
Albanese map Kähler manifolds relative canonical bundle extension theorems

Citation

Păun, Mihai. Relative adjoint transcendental classes and Albanese map of compact Kähler manifolds with nef Ricci curvature. Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, 335--356, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07410335. https://projecteuclid.org/euclid.aspm/1540319496


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