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On a certain algebra associated with a polarized algebraic variety

Published online by Cambridge University Press:  22 January 2016

Hisasi Morikawa
Hisasi Morikawa*
Affiliation:
Nagoya University
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In the present note we associate a certain algebra of finite rank over Q to each non-singular polarized algebraic variety defined over C. For a surface the algebra is a Jordan algebra with identity, and for an abelian variety A the algebra is canonically isomorphic to the Jordan algebra of symmetric elements in EndQ(A) with respect to the involution induced by the polarization. This algebra may be important for a polarized algebraic variety as much as EndQ(A) for an abelian variety A.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 109 - 113
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

1) End Q (A) = End (A) ⊗ zQ, where End (A) means the ring of endomorphisms.