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<p>We complete the classification of all smooth 4-dimensional Kähler 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.</p>

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All Toric Kähler Surfaces with Twistor 2-Forms

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Sergei G. Ovchinnikov

摘要

We complete the classification of all smooth 4-dimensional Kähler 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.