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arXiv · 2004.02682

Holomorphic GL(2)-geometry on compact complex manifolds

Indranil Biswas·Sorin Dumitrescu
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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).

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Indranil Biswas, Sorin Dumitrescu. 2020-04-06. Holomorphic GL(2)-geometry on compact complex manifolds. https://arxiv.org/abs/2004.02682

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