English

Principal polarizations on products of elliptic curves

Algebraic Geometry 2007-05-23 v1 Number Theory

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.

Keywords

Cite

@article{arxiv.math/0508458,
  title  = {Principal polarizations on products of elliptic curves},
  author = {Herbert Lange},
  journal= {arXiv preprint arXiv:math/0508458},
  year   = {2007}
}