不可定向Klein曲面的雅可比矩阵
The Jacobian of a nonorientable Klein surface
摘要：
利用约数，构造了一类紧致连通不可定向Klein曲面$Y$的Jacobian的类似形式.雅可比矩阵被等同于$Y$上所有调和实1-形式空间的对偶，该对偶由$Y$的首次积分同调的无挠部分表示。用$X$表示由定向给出的$Y$的双重覆盖。证明了$Y$的雅可比矩阵是$X$上的所有零次全纯线丛$L$的空间，并证明了$L$同构于$σ^*\bar{L}$，其中$σ$是$X$的对合.
英文摘要：
Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surface $Y$ is constructed. The Jacobian is identified with the dual of the space of all harmonic real one-forms on $Y$ quotiented by the torsion-free part of the first integral homology of $Y$. Denote by $X$ the double cover of $Y$ given by orientation. The Jacobian of $Y$ is identified with the space of all degree zero holomorphic line bundles $L$ over $X$ with the property that $L$ is isomorphic to $σ^*\bar{L}$, where $σ$ is the involution of $X$.
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