Asian Journal of Mathematics

Volume 24 (2020)

Number 5

Complex structures, moment maps, and the Ricci form

Pages: 821 – 854

DOI: https://dx.doi.org/10.4310/AJM.2020.v24.n5.a5

Authors

Oscar García-Prada (Instituto de Ciencias Matemáticas, Madrid, Spain)

Dietmar A. Salamon (Departement Mathematik, Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland)

Samuel Trautwein (Departement Mathematik, Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland)

Abstract

The Ricci form is a moment map for the action of the group of exact volume preserving diffeomorphisms on the space of almost complex structures. This observation yields a new approach to the Weil–Petersson symplectic form on the Teichmüller space of isotopy classes of complex structures with real first Chern class zero and nonempty Kähler cone.

Keywords

moment map, almost complex structure, Ricci form, Teichmüller space

2010 Mathematics Subject Classification

14J10, 53C15, 53D20, 53D35

Received 12 June 2019

Accepted 29 January 2020

Published 10 March 2021