Noether’s Formula, the Picard Scheme, the Albanese Variety, and Plurigenera

  • Lucian Bădescu
Part of the Universitext book series (UTX)


From this point on by surface we mean a nonsingular projective surface X defined over an algebraically closed field k of arbitrary characteristic. When we have to deal with surfaces with singularities, we state that explicitly (for example: let X be a normal surface...).


Abelian Variety Betti Number Group Scheme Invertible Sheaf Quadratic Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographic References

  1. Noether’s formula may be found in [BS].Google Scholar
  2. The Betti numbers of an abstract algebraic surface were originally defined by Igusa (cf. [Igu]); it was later observed that they can also be introduced using étale cohomology, cf. [Del].Google Scholar
  3. Details about the theory of the Picard scheme can be found in [Gro3], [Mural, Mum2], [Ser3], [Oor].Google Scholar
  4. The construction and elementary properties of the Albanese variety can be found in [Ser4].Google Scholar
  5. The Igusa—Severi inequality is proved in [Igu] and [Grob].Google Scholar
  6. The canonical ring of a surface was first considered by Mumford [Mum3].Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Lucian Bădescu
    • 1
  1. 1.Institute of MathematicsRomanian AcademyBucharestRomania

Personalised recommendations