The moduli space of Gieseker vector bundles is a compactification of moduli of vector bundles on a nodal curve. This moduli space has only normal-crossing singularities and it provides flat degeneration of the moduli of vector bundles over a smooth projective curve. We prove a Torelli type theorem for a nodal curve using the moduli space of stable Gieseker vector bundles of fixed rank (strictly greater than 1) and fixed degree such that rank and degree are co-prime.

中文翻译：

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节点曲线的 Torelli 型定理

Gieseker 矢量丛的模空间是节点曲线上矢量丛的模的紧化。这个模空间只有法线交叉奇点，它提供了向量束模在平滑投影曲线上的平坦退化。我们使用固定秩（严格大于1) 和固定度数，使得等级和度数互质。