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Let $C$ be a smooth curve. Letting $J$ be its Jacobian, consider the Poincaré bundle $\mathcal P$ on $J\times J$. Let $p: J\times J\rightarrow J$ be the projection. How can I compute the complex $R p_{*} \mathcal P$ in a point $L\in J$, i.e. what explicitly is

$$R p_\ast \mathcal P_L ?$$

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It is usually a bad idea to ask the question here and on MO at the same time. –  Mariano Suárez-Alvarez Sep 12 '11 at 18:02
As mentioned at MO: there is more than one projection... –  David Roberts Sep 12 '11 at 22:03
say projection onto the first factor. The problem is totally symmetric –  unkn2222 Sep 13 '11 at 13:22

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