The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobian
The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobian
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曲线上向量丛模空间的切线空间和雅可比 theta 除数的奇异轨迹
DOI：
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发表时间：
1998
期刊：
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通讯作者：
E. Izadi
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文献类型：
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作者：
Van Geemen Lambertus;E. Izadi
证明了秩为2的平凡行列式丛的模空间嵌入到Pic^{g-1}C$上线性等价于2\Theta $的线性因子系中.本文证明了半稳定非稳定丛$\xi\oplus\xi^{-1}$（其中$\xi$是零度线丛）上的嵌入切空间由$中的因子组成|2\Theta| $包含$Sing（\Theta_{\xi}）$，其中$\Theta_{\xi}$是$\Theta$通过$\xi$的转换。我们还得到了关于这个切空间的结构的几何结果。
We complete the proof of the fact that the moduli space of rank two bundles with trivial determinant embeds into the linear system of divisors on $Pic^{g-1}C$ which are linearly equivalent to $2\Theta$. The embedded tangent space at a semi-stable non-stable bundle $\xi\oplus\xi^{-1}$, where $\xi$ is a degree zero line bundle, is shown to consist of those divisors in $|2\Theta|$ which contain $Sing(\Theta_{\xi})$ where $\Theta_{\xi}$ is the translate of $\Theta$ by $\xi$. We also obtain geometrical results on the structure of this tangent space.