Non-simple principally polarised abelian varieties

Abstract

The paper investigates the locus of non-simple principally polarised abelian $g$-folds. We show that the irreducible components of this locus are $\Is^g_{D}$, defined as the locus of principally polarised $g$-folds having an abelian subvariety with induced polarisation of type $D=(d_1,\dots ,d_k)$, where $k\le \frac{g}{2}$. The main theorem produces Humbert-like equations for irreducible components of $\Is^g_{D}$ 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.

References in corpus (1)

• Surfaces of general type with $p_g=q=1,K^2=8$ and bicanonical map of degree 2