On coupled constant scalar curvature K\"ahler metrics
Differential Geometry
2019-02-27 v2 Symplectic Geometry
Abstract
We provide a moment map interpretation for the coupled K\"ahler-Einstein equations introduced by Hultgren and Witt Nystr\"om, and in the process introduce a more general system of equations, which we call coupled cscK equations. A differentio-geometric formulation of the corresponding Futaki invariant is obtained and a notion of K-polystability is defined for this new system. Finally, motivated by a result of Sz\'ekelyhidi, we prove that if there is a solution to our equations, then small K-polystable perturbations of the underlying complex structure and polarizations also admit coupled cscK metrics.
Keywords
Cite
@article{arxiv.1901.10454,
title = {On coupled constant scalar curvature K\"ahler metrics},
author = {Ved V. Datar and Vamsi Pritham Pingali},
journal= {arXiv preprint arXiv:1901.10454},
year = {2019}
}
Comments
21 pages. Corrected minor typos, included additional citations, clarified the definition of the coupled Futaki invariant