## On a Shioda-Mitani formula. (Sur une formule de Shioda et Mitani.)(French)Zbl 0699.14038

The author computes for certain abelian surfaces $$X$$ (over the complex numbers $$\mathbb C$$) the numbers of curves $$C$$ whose Jacobians are isomorphic to $$X$$. The $$X$$ under question have multiplication by an indefinite quaternion-algebra, and are simple.
The idea of proof is as follows: One has to classify the principal polarisations on $$X$$. This becomes a problem in the arithmetic of quaternions, and is governed by certain class numbers.

### MSC:

 14H40 Jacobians, Prym varieties 14K22 Complex multiplication and abelian varieties 11G10 Abelian varieties of dimension $$> 1$$ 11G18 Arithmetic aspects of modular and Shimura varieties 14K05 Algebraic theory of abelian varieties
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### References:

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