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, Volume 159, Issue 1–2, pp 39–56 | Cite as

2-Nilpotent co-Higgs structures

  • Edoardo Ballico
  • Sukmoon HuhEmail author


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.

Mathematics Subject Classification

Primary: 14J60 Secondary: 14D20 53D18 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università di TrentoPovoItaly
  2. 2.Sungkyunkwan UniversitySuwonKorea

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