Gaussian maps, Gieseker-Petri loci and large theta-characteristics
Gaussian maps, Gieseker-Petri loci and large theta-characteristics
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高斯图、Giesker-Petri 轨迹和大 theta 特征
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发表时间：
2005
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通讯作者：
G. Farkas
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作者：
G. Farkas
对于整数g≥1，我们考虑参数化偶(C，L)的光滑自旋曲线的模空间Sg，其中C是亏格为g的光滑曲线，L是特征，即C上的线丛使得L2∼=Kc.众所周知，自然映射π：Sg→mg是2次2g的有限的，Sg是两个分支S7g和S奇数g的不相交并，对应于奇偶特征。利用亏格g(cf.)的稳定自旋曲线，Cornalba构造了具有几何意义的Sg的紧化。[C])。亏格的稳定的n点r-自旋曲线的空间Sg和更一般的模空间S 1/rg，n，具有标准丛的r-根的参数化点曲线，近年来引起了人们的极大关注
For an integer g ≥ 1 we consider the moduli space Sg of smooth spin curves parametrizing pairs (C,L), where C is a smooth curve of genus g and L is a thetacharacteristic, that is, a line bundle on C such that L2 ∼= KC . It has been known classically that the natural map π : Sg → Mg is finite of degree 2 2g and that Sg is a disjoint union of two components Seven g and S odd g corresponding to even and odd theta-characteristics. A geometrically meaningful compactification Sg of Sg has been constructed by Cornalba by means of stable spin curves of genus g (cf. [C]). The space Sg and more generally the moduli spaces S 1/r g,n of stable n-pointed r-spin curves of genus g, parametrizing pointed curves with r-roots of the canonical bundle, have attracted a lot of attention in recent