Skip to main content
SpringerLink
Log in

On the stability of tangent bundle on double coverings

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let τ: X → Y be a double covering branched along a smooth divisor. We show that I X is stable with respect to τ*H if the tangent bundle I Y is semi-stable with respect to some ample line bundle H on Y.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barth, W. P., Hulek, K., Peters, C. A. M., et al.: Complex Compact Surfaces, Springer Science & Business Media, Berlin, 2004

    Book  MATH  Google Scholar 

  2. Friedman, R.: Algebraic Surfaces and Holomorphic Vector Bundles, Springer Science & Business Media, New York, 2012

    Google Scholar 

  3. Gieseker, D.: On a theorem of Bogomolov on Chern classes of stable bundles. Amer. J. Math., 101, 77–85 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Huybrechts, D., Lehn, M.: The Geometry of Moduli Spaces of Sheaves, Cambridge University Press, Cambridge, 2010

    Book  MATH  Google Scholar 

  5. Huybrechts, D.: Lectures on K3 Surfaces, Cambridge University Press, Cambridge, 2016

    Book  MATH  Google Scholar 

  6. Joshi, K., Ramanan, S., Xia, E. Z., et al.: On vector bundles destabilized by Frobenius pull-back. Compos. Math., 142, 616–630 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Katz, N. M.: Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin. Publ. Math., Inst. Hautes, Études Sci., 39, 175–232 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, L., Shentu, J.: Strong stability of cotangent bundles of cyclic covers. C. R. Math. Acad. Sci. Paris, 352(7), 639–644 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun, X.: Direct images of bundles under Frobenius morphism. Invent. Math., 173, 427–447 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author would like to express sincere thanks to his advisor Professor Xiaotao Sun for careful reading and helpful discussions to improve the paper in both mathematics and presentations.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    Yongming Zhang

Authors
  1. Yongming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongming Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Y. On the stability of tangent bundle on double coverings. Acta. Math. Sin.-English Ser. 33, 1039–1047 (2017). https://doi.org/10.1007/s10114-017-6190-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-017-6190-7

Keywords

MR(2010) Subject Classification

Search

Navigation