Principal polarizations on products of elliptic curves

2005/08/24 by Herbert Lange, Lange, Herbert · 1 citation
Mathematics · #11G10 #14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G10 #msc:14K05

paper · pdf · doi:10.48550/arxiv.math/0508458

arxiv created 2005/08/24 · arxiv updated 2009/12/01

Abstract

An abelian variety admits only a finite number of isomorphism classes of principal polarizations. The paper gives an interpretation of this number in terms of class numbers of definite Hermitian forms in the case of a product of elliptic curves without complex multiplication. In the case of a self-product of an elliptic curve, as well as in the two-dimensional case, classical class number computations can be applied to determine this number.

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