IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v298y2025i1p6-52.html
   My bibliography  Save this article

On K3 surfaces of Picard rank 14

Author

Listed:
  • Adrian Clingher
  • Andreas Malmendier

Abstract

We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank 14, 2‐elementary lattices. Three such lattices exist, namely, H⊕E8(−1)⊕A1(−1)⊕4$H \oplus E_8(-1) \oplus A_1(-1)^{\oplus 4}$, H⊕E8(−1)⊕D4(−1)$H \oplus E_8(-1) \oplus D_4(-1)$, and H⊕D8(−1)⊕D4(−1)$H \oplus D_8(-1) \oplus D_4(-1)$. As part of our study, we provide birational models for these surfaces as quartic projective hypersurfaces and describe the associated coarse moduli spaces in terms of suitable modular invariants. Additionally, we explore the connection between these families and dual K3 families related via the Nikulin construction.

Suggested Citation

  • Adrian Clingher & Andreas Malmendier, 2025. "On K3 surfaces of Picard rank 14," Mathematische Nachrichten, Wiley Blackwell, vol. 298(1), pages 6-52, January.
  • Handle: RePEc:bla:mathna:v:298:y:2025:i:1:p:6-52
    DOI: 10.1002/mana.202200197
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202200197
    Download Restriction: no

    File URL: https://libkey.io/10.1002/mana.202200197?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    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:bla:mathna:v:298:y:2025:i:1:p:6-52. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.