Skip to main content
SpringerLink
Log in

Exceptional sets on del Pezzo surfaces with one log-terminal singularity

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

New full exceptional sets of coherent sheaves on a certain family of log-terminal del Pezzo surfaces, which is treated as a smooth stack, are constructed. These surfaces are not toroidal and can be represented as hypersurfaces in weighted projective 3-space.

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. D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves,” Izv. Ross. Akad. Nauk. Ser. Mat. 56 (4), 852–862 (1992) [Russian Acad. Sci. Izv. Math. 41(1), 133–141 (1993)].

    Google Scholar 

  2. S. A. Kuleshov and D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces,” Izv. Ross. Akad. Nauk. Ser. Mat. 58(3), 53–87 (1994) [Russian Acad. Sci. Izv. Math. 44 (3), 479–513(1995)].

    MathSciNet  Google Scholar 

  3. Y. Kawamata, Derived Categories of Toric Varieties, arxiv: math. AG/0503102.

  4. D. Auroux, L. Katzarkov, and D. Orlov, Mirror Symmetry for Weighted Projective Planes and Their Noncommutative Deformations, arxiv: math. AG/0404281.

  5. A. I. Bondal, “Representations of associative algebras and coherent sheaves,” Izv. Acad. Nauk SSSR. Ser. Mat. 53 (1), 25–44 (1989) [Math. USSR-Izv. 34 (1), 23–42 (1990)].

    MathSciNet  Google Scholar 

  6. W. Fulton, Introduction to Toric Varieties (Princeton Univ. Press, Princeton, NJ, 1993).

    MATH  Google Scholar 

  7. R. Hartshorne, Algebraic Geometry (Springer, New York, 1977; Mir, Moscow, 1981).

    MATH  Google Scholar 

  8. H. Kojima, “Logarithmic Del Pezzo surfaces of rank one with unique singular points,” Japan. J. Math. (N. S.) 25 (2), 343–375 (1999).

    MATH  MathSciNet  Google Scholar 

  9. M. Artin and J. J. Zhang, “Noncommutative Projective Schemes,” Adv. Math. 109 (2), 228–287 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Baer, “Tilting sheaves in representation theory of algebras,” Manuscripta Math. 60 (3), 323–347 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Keller, “Derived categories and their uses,” in Handbook of Algebra (North-Holland, Amsterdam, 1996), Vol. 1, pp. 671–701.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Russia

    A. D. Elagin

Authors
  1. A. D. Elagin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. D. Elagin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Elagin, A.D. Exceptional sets on del Pezzo surfaces with one log-terminal singularity. Math Notes 82, 33–46 (2007). https://doi.org/10.1134/S000143460707005X

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000143460707005X

Key words

Search

Navigation