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.

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**Knowl status:**

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

**Referred to by:**

- ag.canonical_height
- av.fq.isogeny_class_size
- av.hyperelliptic_count
- av.jacobian_count
- columns.av_fq_isog.has_principal_polarization
- hmsurface.component_ideal
- lmfdb/abvar/fq/main.py (line 373)
- lmfdb/abvar/fq/stats.py (line 53)
- lmfdb/abvar/fq/stats.py (line 126)
- lmfdb/abvar/fq/templates/show-abvarfq.html (lines 68-73)
- lmfdb/abvar/fq/templates/show-abvarfq.html (lines 152-165)

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