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...).


Posites Stein Betti Neron 


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