Annals of Global Analysis and Geometry

, Volume 23, Issue 2, pp 189–204 | Cite as

Compact Kähler Surfaces with Trivial Canonical Bundle

  • Nicholas Buchdahl


The classical conjectures of Weil on K3 surfaces – that the set of suchsurfaces is connected; that a version of the Torelli theorem holds; thateach such surface is Kähler; and that the period map issurjective – are reconsidered in the light of a generalisation of theNakai–Moishezon criterion, and short proofs of all the conjectures aregiven. Most of the proofs apply equally or with minor variation tocomplex 2-tori, the only other compact Kähler surfaces with trivialcanonical bundle.

Kähler surface K3 surface complex 2-torus period map Torelli theorem 


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© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Nicholas Buchdahl
    • 1
  1. 1.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia

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