IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4613-8655-1_4.html
   My bibliography  Save this book chapter

Abelian Varieties over ℂ

In: Arithmetic Geometry

Author

Listed:
  • Michael Rosen

Abstract

These lecture notes present, in outline, the theory of abelian varieties over the complex numbers. They focus mainly on the analytic side of the subject. In the first section we prove some basic results on complex tori. The second section is devoted to a discussion of isogenics. The third section (the longest) describes the necessary and sufficient conditions that a complex torus must satisfy in order to be isomorphic to an abelian variety. In the fourth section we describe the construction of the dual abelian variety and the concluding two sections discuss polarizations and the moduli space of principally polarized abelian varieties. Proofs for the most part are omitted or only sketched. Details can be found in [SW] or [L-A] (see the list of references at the end of this chapter). For the algebraic-geometric study of abelian varieties over arbitrary fields, the reader is referred to [M-AV] and to the articles of J. S. Milne in this volume.

Suggested Citation

  • Michael Rosen, 1986. "Abelian Varieties over ℂ," Springer Books, in: Gary Cornell & Joseph H. Silverman (ed.), Arithmetic Geometry, chapter 0, pages 79-101, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8655-1_4
    DOI: 10.1007/978-1-4613-8655-1_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4613-8655-1_4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.