All toric Kahler surfaces with twistor 2-forms

Sergei G. Ovchinnikov

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arXiv · 2412.21114

All toric Kahler surfaces with twistor 2-forms

Sergei G. Ovchinnikov

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Abstract

We complete the classification of all smooth 4-dimensional Kahler geometries admitting a twistor (conformal Killing-Yano) 2-form invariant under a 2-torus action. We establish that there are six geometrically distinct families, and we provide them in a simple form amenable to calculations and compute their curvature. We also find that for toric geometries the square norm of the twistor 2-form is quadratic in moment maps, and we are led to conjecture that this holds when less symmetry is present.

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Sergei G. Ovchinnikov. 2024-12-30. All toric Kahler surfaces with twistor 2-forms. https://arxiv.org/abs/2412.21114

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