On coupled constant scalar curvature K\'ahler metrics

Autor:	Datar, Ved V., Pingali, Vamsi Pritham
Rok vydání:	2019
Předmět:	Mathematics - Differential Geometry Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages. Corrected minor typos, included additional citations, clarified the definition of the coupled Futaki invariant
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.10454 Zobrazit plný text záznamu View this record from Arxiv