×

zbMATH — the first resource for mathematics

Abelian surfaces admitting an \((l,l)\)-endomorphism. (English) Zbl 1316.14085
Summary: We give a classification of all principally polarized abelian surfaces that admit an \((l,l)\)-isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case \(l=2\). As part of our classification, we also show how to find all principally polarized abelian surfaces with multiplication by a given imaginary quadratic order.

MSC:
14K02 Isogeny
14C20 Divisors, linear systems, invertible sheaves
Software:
Echidna
PDF BibTeX XML Cite
Full Text: DOI arXiv