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Archiv der Mathematik

, 93:437 | Cite as

Semistability and finite maps

  • Indranil Biswas
  • S. Subramanian
Article

Abstract

Let \({f : Y \longrightarrow M}\) be a surjective holomorphic map between compact connected Kähler manifolds such that each fiber of f is a finite subset of Y. Let ω be a Kähler form on M. Using a criterion of Demailly and Paun (Ann. Math. 159 (2004), 1247–1274) it follows that the form f*ω represents a Kähler class. Using this we prove that for any semistable sheaf \({E\, \longrightarrow\,M}\) , the pullback f*E is also semistable. Furthermore, f*E is shown to be polystable provided E is reflexive and polystable. These results remain valid for principal bundles on M and also for Higgs G-sheaves.

Mathematics Subject Classification (2000)

Primary 32L05 Secondary 53C07 

Keywords

Einstein–Hermitian connection Semistable bundle Finite map 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia

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