Skip to main content
SpringerLink
Log in

Derived categories of nodal curves

  • Published:
Ukrainian Mathematical Journal Aims and scope

We describe derived categories of coherent sheaves over nodal noncommutative curves of string and almost string types.

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. Yu. A. Drozd and D. E. Voloshyn, “Vector bundles over noncommutative nodal curves,” Ukr. Mat. Zh., 64, No. 2, 185–199 (2012); English translation: Ukr. Math. J., 64, No. 2, 208–224 (2012).

    Article  MATH  Google Scholar 

  2. Y. Drozd and G.-M. Greuel, “Tame and wild projective curves and classification of vector bundles,” J. Algebra, 246, No. 1, 1–54 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Drozd, G.-M. Greuel, and I. Kashuba, “On Cohen–Macaulay modules on surface singularities,” Moscow Math. J., 3, No. 2, 397–418 (2003).

    MathSciNet  MATH  Google Scholar 

  4. W. Geigle and H. Lenzing, “A class of weighted projective curves arising in representation theory of finite-dimensional algebras,” in: Singularities, Representations of Algebras, and Vector Bundles (Lambrecht, 1985), Springer, Berlin (1987), pp. 265–297.

    Chapter  Google Scholar 

  5. I. Burban and Y. Drozd, “Coherent sheaves on rational curves with simple double points and transversal intersections,” Duke Math. J., 21, No. 2, 129–229 (2004).

    MathSciNet  Google Scholar 

  6. R. Hartshorne, Algebraic Geometry, Springer, Berlin (1977).

    MATH  Google Scholar 

  7. H. Lenzing, “Hereditary categories,” in: L. A. Hügel, D. Happel, and H. Krause (editors), Handbook of Tilting Theory, Cambridge University, Cambridge (2007), pp. 105–146.

    Chapter  Google Scholar 

  8. Yu. A. Drozd, V. V. Kirichenko, and A. V. Roiter, “On the hereditary and Bass orders,” Izv. Akad. Nauk SSSR, Ser. Mat., 31, No. 6, 1415–1436 (1967).

    MathSciNet  MATH  Google Scholar 

  9. V. M. Bondarenko, “Representations of the bundles of semichained sets and their applications,” Alg. Analiz, 3, No. 5, 38–61 (1991).

    MathSciNet  MATH  Google Scholar 

  10. I. Burban and Y. Drozd, “Derived categories of nodal algebras,” J. Algebra, 272, No. 1, 46–94 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  11. D. E. Voloshyn, “Structure of nodal algebras,” Ukr. Mat. Zh., 63, No. 7, 880–888 (2011); English translation: Ukr. Math. J., 63, No. 7, 1013–1022 (2011).

    Article  MATH  Google Scholar 

  12. Y. A. Drozd, “Derived tame and derived wild algebras,” Alg. Discr. Math., No. 1, 54–74 (2004).

    Google Scholar 

  13. A. Neeman, Triangulated Categories, Princeton University, Princeton (2001).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    D. E. Voloshyn & Yu. A. Drozd

Authors
  1. D. E. Voloshyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Drozd
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 8, pp. 1033–1040, August, 2012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voloshyn, D.E., Drozd, Y.A. Derived categories of nodal curves. Ukr Math J 64, 1177–1184 (2013). https://doi.org/10.1007/s11253-013-0708-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-013-0708-7

Keywords

Search

Navigation