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An abelian variety is principally polarizable if it admits a polarization that is an isomorphism. For example, the Jacobian of a curve admits a canonical principal polarization; by the Torelli theorem, the curve is uniquely determined by its Jacobian together with this polarization.

An isogeny class of abelian varieties is principally polarizable if one of its members admits a principal polarization.

Knowl status:
  • Review status: reviewed
  • Last edited by Kiran S. Kedlaya on 2019-05-04 20:27:23
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