Holomorphic GL(2)-geometry on compact complex manifolds
Differential Geometry
2020-08-12 v2 Algebraic Geometry
Abstract
We study holomorphic GL(2) and SL(2) geometries on compact complex manifolds. We show that a compact K\"ahler manifold of complex even dimension higher than two admitting a holomorphic GL(2)-geometry is covered by a compact complex torus. We classify compact K\"ahler-Einstein manifolds and Fano manifolds bearing holomorphic GL(2)-geometries. Among the compact K\"ahler-Einstein manifolds we prove that the only examples bearing holomorphic GL(2)-geometry are those covered by compact complex tori, the three dimensional quadric and those covered by the three dimensional Lie ball (the non compact dual of the quadric).
Cite
@article{arxiv.2004.02682,
title = {Holomorphic GL(2)-geometry on compact complex manifolds},
author = {Indranil Biswas and Sorin Dumitrescu},
journal= {arXiv preprint arXiv:2004.02682},
year = {2020}
}
Comments
This is the final version to be published in Manuscripta Mathematica