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arXiv · 2509.01639

Toric geometry of generalized K\"ahler-Ricci solitons

Vestislav Apostolov·Giuseppe Barbaro·Jeffrey Streets·Yury Ustinovskiy
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Abstract

We establish a local equivalence between toric steady K\"ahler-Ricci solitons and $A$-type toric generalized K\"ahler-Ricci solitons (GKRS). Under natural global conditions we show this equivalence extends to complete GKRS, yielding a general construction of new examples in all dimensions. We show that in four dimensions, all GKRS are either described by the generalized K\"ahler Gibbons-Hawking ansatz, or have split tangent bundle, or are $A$-type toric. This yields a local classification in four dimensions, together with a conjecturally exhaustive construction of complete symplectic-type examples.

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Vestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets, Yury Ustinovskiy. 2025-09-01. Toric geometry of generalized K\"ahler-Ricci solitons. https://arxiv.org/abs/2509.01639

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