Abstract
Let \(({{\mathcal {E}}}, \phi )\) be a rank two co-Higgs vector bundles on a Kähler compact surface X with \(\phi \in H^0(X,End({{\mathcal {E}}})\otimes T_X)\) nilpotent. If \(({{\mathcal {E}}}, \phi )\) is semi-stable, then one of the following holds up to finite étale cover: (1) X is uniruled. (2) X is a torus and \(({{\mathcal {E}}}, \phi )\) is strictly semi-stable. (3) X is a properly elliptic surface and \(({{\mathcal {E}}}, \phi )\) is strictly semi-stable.
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Acknowledgments
We are grateful to Arturo Fernandez-Perez, Renato Martins and Marcos Jardim for pointing out corrections. We are grateful to Henrique Bursztyn for interesting conversations about Poisson Geometry.
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Dedicated to Jose Seade, for his 60th birthday.
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Corrêa, M. Rank two nilpotent co-Higgs sheaves on complex surfaces. Geom Dedicata 183, 25–31 (2016). https://doi.org/10.1007/s10711-016-0141-9
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DOI: https://doi.org/10.1007/s10711-016-0141-9