The geometry of the moduli space of odd spin curves
The geometry of the moduli space of odd spin curves
复制标题
奇自旋曲线模空间的几何
DOI：
10.4007/annals.2014.180.3.3
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发表时间：
2010
影响因子：
4.9
通讯作者：
A. Verra
中科院分区：
文献类型：
--
作者：
G. Farkas;A. Verra
自旋模spaceSg是g属稳定曲线上的特征（自旋结构）的参数空间，它有两个相连的分量Sg和+ g，取决于自旋结构的宇称。利用自旋模空间奇分量g的Kodaira维建立了一个完全的两族分类。我们证明g在g < 12时是无序的，在g < 8时甚至是无序的。在此范围内，对一维线性截面为g属一般正则曲线的Mukai变种引入聚类的概念，构造了新的g属双域模型。然后我们用这些来明确地描述S g的双族结构。例如，在具有七对标记点的椭圆曲线的模空间上，s8与一个局部平凡p7 -束是二乘的。对于g12，我们证明了g是一般类型的变种。在属12的稳定曲线的模空间上，这需要构造一个关于有效因子的斜率猜想的反例。
The spin moduli spaceSg is the parameter space of theta characteristics (spin structures) on stable curves of genus g. It has two connected components, S g andS + g , depending on the parity of the spin structure. We establish a complete birational classication by Kodaira dimension of the odd componentS g of the spin moduli space. We show thatS g is uniruled for g < 12 and even unirational for g 8. In this range, introducing the concept of cluster for the Mukai variety whose one-dimensional linear sections are general canonical curves of genus g, we construct new birational models ofS g . These we then use to explicitly describe the birational structure of S g . For instance, S 8 is birational to a locally trivial P 7 -bundle over the moduli space of elliptic curves with seven pairs of marked points. For g 12, we prove thatS g is a variety of general type. In genus 12, this requires the construction of a counterexample to the Slope Conjecture on eective divisors on the moduli space of stable curves of genus 12.
Prym 品种模空间的 Kodaira 维数
影响因子：
2.6
作者：
Farkas;Gavril;Ludwig;Katharina
通讯作者：
Katharina