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arXiv · 1307.6591

Non-simple principally polarised abelian varieties

Paweł Borówka
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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 $D=(d_1,\ldots,d_k)$, where $k\leq\frac{g}{2}$. 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 \'etale double covers or double covers branched in two or four points.

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Paweł Borówka. 2013-07-24. Non-simple principally polarised abelian varieties. https://doi.org/10.1007/s10231-015-0527-6

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