https://neckpinch.com/authors/giuseppe-barbaro/New arXiv papers by Giuseppe Barbaro, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2509.01639/arxiv:2509.01639Mon, 01 Sep 2025 00:00:00 GMTVestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets, Yury Ustinovskiy — We establish a local equivalence between toric steady Kähler-Ricci solitons and A-type toric generalized Kähler-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 Kähler 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.Ricci solitonsKähler–Ricci solitonsKähler geometry https://neckpinch.com/papers/2402.03996/arxiv:2402.03996Tue, 06 Feb 2024 00:00:00 GMTMichael Albanese, Giuseppe Barbaro, Mehdi Lejmi — We generalize Kähler-Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map, and show that their existence is an obstruction to the existence of first-Chern-Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the 4-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on 2n-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler-Ricci solitons. In particular, we partially extend Matsushima's theorem to compact first-Chern-Einstein almost-Kähler manifolds.Ricci solitonsKähler–Ricci solitonsKähler geometry