Abstract
A co-Higgs sheaf on a smooth complex projective variety X is a pair of a torsion-free coherent sheaf \(\mathcal {E}\) and a global section of \(\mathcal {E}nd(\mathcal {E})\otimes T_X\) with \(T_X\) the tangent bundle. We construct 2-nilpotent co-Higgs sheaves of rank two for some rational surfaces and of rank three for \(\mathbb {P}^3\), using the Hartshorne-Serre correspondence. Then we investigate the non-existence, especially over projective spaces.
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The first author is partially supported by MIUR, GNSAGA of INDAM (Italy) and PRIN 2015 “Geometria delle varietà algebriche”, cofinanced by MIUR. The second author is supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2018R1C1A6004285 and No. 2016R1A5A1008055).
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Ballico, E., Huh, S. 2-Nilpotent co-Higgs structures. manuscripta math. 159, 39–56 (2019). https://doi.org/10.1007/s00229-018-1045-9
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DOI: https://doi.org/10.1007/s00229-018-1045-9