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Divisorial properties and special metrics on hypercomplex twistor spaces

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arxiv 2410.19490 v1 pith:E75EEQMT submitted 2024-10-25 math.AG math.CVmath.DG

Alberto Pipitone Federico This is my paper · ORCID
classification math.AGmath.CVmath.DG
keywords provefiberhlerhypercomplexmetricssamespacestwistor
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We prove that the general fiber of a compact hypercomplex twistor space with a K\"{a}hler fiber has no divisors nor curves. This is first used to prove that, under the same assumption, the trascendental degree of the field of meromoprhic functions is one. The same result allows to prove that these spaces admit no K\"{a}hler and not even pluriclosed metrics.

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Cited by 1 Pith paper

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  1. Exotic hypercomplex structures on a torus do not exist

    math.DG 2025-06 conditional novelty 7.0 of 10

    Exotic hypercomplex structures do not exist on complex tori; every hypercomplex structure there is hyperkähler.

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