Picard Group - Examples

Examples

  • The Picard group of the spectrum of a Dedekind domain is its ideal class group.
  • The invertible sheaves on projective space Pn(k) for k a field, are the twisting sheaves so the Picard group of Pn(k) is isomorphic to Z.
  • The Picard group of the affine line with two origins over k is isomorphic to Z.

Read more about this topic:  Picard Group

Famous quotes containing the word examples:

    Histories are more full of examples of the fidelity of dogs than of friends.
    Alexander Pope (1688–1744)

    No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.
    André Breton (1896–1966)

    It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.
    —G.C. (Georg Christoph)