一个推广的Abel-Jacobi映射
An Extended Abel-Jacobi Map
摘要：
我们解决了一个扩展的Abel-Jacobi映射$$ \int_{P_{0}}^{P_{1}}ω+...+\int_{P_{0}}^{P_{g+n-1}}ω={\bf z}, \qquad \int_{P_{0}}^{P_{1}}Ω_{j1}+... +\int_{P_{0}}^{P_{g+n-1}}Ω_{j1} =Z_{j},\quad j=2,...,n, $$的反演问题，其中$Ω_{j1}$是第三类（归一化）阿贝尔微分。在对比的扩展已经研究，这一个包含亚纯微分有一个共同的极点$Q_1$。这个反演问题出现在单极子的代数几何描述中，以及在loop代数上的有限维未约余伴轨道上的可积系统的线性化中。
英文摘要：
We solve the problem of inversion of an extended Abel-Jacobi map $$ \int_{P_{0}}^{P_{1}}ω+...+\int_{P_{0}}^{P_{g+n-1}}ω={\bf z}, \qquad \int_{P_{0}}^{P_{1}}Ω_{j1}+... +\int_{P_{0}}^{P_{g+n-1}}Ω_{j1} =Z_{j},\quad j=2,...,n, $$ where $Ω_{j1}$ are (normalised) abelian differentials of the third kind. In contrast to the extensions already studied, this one contains meromorphic differentials having a common pole $Q_1$. This inversion problem arises in algebraic geometric description of monopoles, as well as in the linearization of integrable systems on finite-dimensional unreduced coadjoint orbits on loop algebras.
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