A stratification of \(B^4(2,K_C)\) over a general curve

  • Abel Castorena
  • Graciela Reyes-Ahumada
Original Article


Let C be a smooth curve of genus \(g\ge 10\) with general moduli. We show that the Brill–Noether locus \(B^4(2,K_C)\) contains irreducible subvarieties \({\mathcal {B}}_3\supset {\mathcal {B}}_4\supset \cdots \supset {\mathcal {B}}_n\), where each \({\mathcal {B}}_k\) has dimension \(3g-10-k\) and \({\mathcal {B}}_3\) is an irreducible component of the expected dimension the Brill–Noether number \(\rho =3g-13\).


Vector bundles Brill–Noether loci Moduli of curves 

Mathematics Subject Classification

Primary 14C20 Secondary 14H60 14J26 



  1. 1.
    Arbarello, E., Cornalba, M., Griffiths, P., Harris, J.: Geometry of Algebraic Curves Volume I. Series: Grundlehren der mathematischen Wissenschaften, vol. 267. Springer, New York (1985)CrossRefGoogle Scholar
  2. 2.
    Castorena, A., Reyes-Ahumada, G.: Rank two bundles with canonical determinant and four sections. Rendiconti del Circolo Matematico di Palermo (1952 -). 64(2), 261–272 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ciliberto, C., Flamini, F.: Extensions of line bundles and Brill-Noether loci of rank-two vector bundles on a general curve. Rev. Rumaine Math. Pures Appl. 60(3), 201–255 (2015)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Gieseker, D.: A lattice version of the KP equation. Acta Math. 168, 219–248 (1992)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lange, H.: Higher secant varieties of curves and the theorem of Nagata on ruled surfaces. Manuscripta Math. 47, 263 (1984). MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Lange, H., Narasimhan, M.S.: Maximal subbundles of rank two vector bundles on curves. Math. Ann. 266(1), 55–72 (1983)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics, vol. 52. Springer, Heidelberg (1977)CrossRefGoogle Scholar
  8. 8.
    Sernesi, E.: Deformations of Algebraic Schemes. Volume 334, Grundlehren der mathematischen Wissenschaften. A Series of Comprehensive Studies in Mathematics. Springer, Berlin (2006)Google Scholar

Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México), Campus MoreliaMoreliaMexico
  2. 2.Cátedra CONACYT-UAZ, Unidad Académica de Matemáticas, Paseo la Bufa, Calzada SolidaridadZacatecasMexico

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