Non-simple principally polarised abelian varieties

Bibliographic description

punktacja MNiSW [2016 A]: 30

title:	Non-simple principally polarised abelian varieties
author:	Borówka Paweł
journal title:	Annali di Matematica Pura ed Applicata
volume:	195
issue:	5
date of publication :	2016
pages:	1531-1549
ISSN:	0373-3114
eISSN:	1618-1891
DOI:	10.1007/s10231-015-0527-6
language:	English
journal language:	English
abstract in English:	The paper investigates the locus of non-simple principally polarised abelian g-folds. We show that the irreducible components of this locus are IsgD, defined as the locus of principally polarised g-folds having an abelian subvariety with restricted polarisation of type D=(d1,…,dk), where k≤g2. The main theorem produces Humbert-like equations for irreducible components of IsgD for any g and D. Moreover, there are theorems which characterise the Jacobians of curves that are étale double covers or double covers branched in two or four points.
keywords in English:	non-simple abelian varieties, equations in the Siegel space, Humbert locus, Prym–Tyurin varieties
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper