We show that the only summands of theta divisors on Jacobians of curves and intermediate Jacobians of cubic threefolds are the obvious powers of the curve and the Fano surface of lines on the threefold. The proof uses the decomposition theorem for perverse sheaves, some representation theory and a computation of characteristic cycles for Brill-Noether sheaves.

中文翻译：

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雅可比的 theta 除数的总和

我们表明，曲线的雅可比曲线和三次三次的中间雅可比矩阵的 theta 除数的唯一和是曲线的明显幂和三重曲线的 Fano 曲面。该证明使用了反常滑轮的分解定理、一些表示理论和 Brill-Noether 滑轮的特征周期计算。