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Holomorphic GL(2)-geometry on compact complex manifolds | | Indranil Biswas
; Sorin Dumitrescu
; | | Date: |
6 Apr 2020 | | 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). | | Source: | arXiv, 2004.2682 | | Services: | Forum | Review | PDF | Favorites | |
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