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Higher rank BN-theory for curves of genus 5

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Abstract

In this paper, we consider higher rank Brill–Noether theory for smooth curves of genus 5, obtaining new upper bounds for non-emptiness of Brill–Noether loci and many new examples.

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References

  1. Ballico, E.: Brill-Noether theory for vector bundles on projective curves. Proc. Camb. Philos. Soc. 128, 483–499 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bertram, A., Feinberg, B.: On stable rank two bundles with canonical determinant and many sections, in Algebraic Geometry (Catania, 1993/Barcelona 1994), Lecture Notes in Pure and Appl. Math., vol. 200. Marcel Dekker, New York, pp. 259–269 (1998)

  3. Bhosle, U.N., Brambila-Paz, L., Newstead, P.E.: On linear series and a conjecture of D. C. Butler. Int. J. Math. 26(1), 1550007 (2015). doi:10.1142/S0129167X1550007X

    Article  MathSciNet  MATH  Google Scholar 

  4. Brambila-Paz, L., Grzegorczyk, I., Newstead, P.E.: Geography of Brill–Noether loci for small slopes. J. Algebr. Geom. 6, 645–669 (1997)

    MathSciNet  MATH  Google Scholar 

  5. Brambila-Paz, L., Mercat, V., Newstead, P.E., Ongay, F.: Nonemptiness of Brill–Noether loci. Int. J. Math. 11, 737–760 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Butler, D.C.: Birational maps of moduli of Brill-Noether pairs. arXiv:alg-geom/9705009v1

  7. Lange, H., Newstead, P.E.: Bundles computing Clifford indices on trigonal curves. Arch. Math. 101, 21–31 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lange, H., Newstead, P.E.: Vector bundles of rank \(2\) computing Clifford indices. Commun. Algebra 41, 2317–2345 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lange, H., Newstead, P.E.: Higher rank BN-theory for curves of genus \(4\). arXiv:1511.02925

  10. Mercat, V.: Le problème de Brill–Noether pour des fibrés stables de petite pente. J. Reine Angew. Math. 506, 1–41 (1999)

    MathSciNet  Google Scholar 

  11. Mercat, V.: Le problème de Brill–Noether et le théorème de Teixidor. Manuscr. math. 98, 75–85 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mercat, V.: Fibrés stables de pente 2. Bull. Lond. Math. Soc. 33, 535–542 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mercat, V.: Clifford’s theorem and higher rank vector bundles. Int. J. Math. 13, 785–796 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Re, R.: Multiplication of sections and Clifford bounds for stable vector bundles on curves. Commun. Algebra 26, 1931–1944 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Teixidor i Bigas, M.: Brill–Noether theory for stable vector bundles. Duke Math. J 62, 385–400 (1991)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Cauerstraße 11, 91058, Erlangen, Germany

    H. Lange

  2. Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool, L69 7ZL, UK

    P. E. Newstead

Authors
  1. H. Lange
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  2. P. E. Newstead
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Correspondence to H. Lange.

Additional information

H. Lange and P. E. Newstead are members of the research group VBAC (Vector Bundles on Algebraic Curves). P. E. Newstead would like to thank the Department Mathematik der Universität Erlangen-Nürnberg for its hospitality.

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Lange, H., Newstead, P.E. Higher rank BN-theory for curves of genus 5. Rev Mat Complut 29, 691–717 (2016). https://doi.org/10.1007/s13163-016-0203-4

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  • DOI: https://doi.org/10.1007/s13163-016-0203-4

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