We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.

中文翻译：

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二次曲面中包含的三类曲线的稳定滑轮的模量

我们研究了在光滑二次曲面中包含的算术属3的曲线上支撑的欧拉特性1的稳定滑轮的模空间。我们证明该模空间是有理的。我们通过研究α-半稳定对的模空间的变化来计算其贝蒂数。我们使用本地免费的分辨率或扩展名对稳定轮进行分类。我们给出一个整体描述：模空间是通过执行两次翻转然后放空从某个标志的希尔伯特方案获得的。