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Some intersections in the Poincare bundle, and the universal theta divisor on the moduli space of (semi)abelian varieties

Samuel Grushevsky·David Lehavi
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Abstract

We compute all the top intersection numbers of divisors on the total space of the Poincare bundle restricted to the product of a curve and the abelian variety. We use these computations to find the class of the universal theta divisor and $m$-theta divisor inside the universal corank 1 semiabelian variety -- the boundary of the partial toroidal compactification of the moduli space of abelian varieties. We give two computational examples: we compute the boundary coefficient of the Andreotti-Mayer divisor (computed by Mumford but in a much harder and ad hoc way), and the analog of this for the universal $m$-theta divisor.

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Samuel Grushevsky, David Lehavi. 2007-10-20. Some intersections in the Poincare bundle, and the universal theta divisor on the moduli space of (semi)abelian varieties. https://doi.org/10.1093/imrn%2Frnm128

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