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arXiv 1102.07152011-02-15math.ATmath.AG

r-自旋Riemann surfaces模空间的Picard群

The Picard group of the moduli space of r-Spin Riemann surfaces

Oscar Randal-Williams

备注：: v2: Fixed some formulae and improved Theorem 1.15
发表信息：: Adv. Math. 231 (2012), no. 1, 482--515
DOI：: 10.1016/j.aim.2012.04.027

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摘要：

最近我们证明了r-SpinRiemann曲面的模空间的一个同调稳定性定理，特别地，它蕴涵了这些模空间的一个Madsen-Weiss定理.这使得我们能够有效地研究它们的稳定上同调，并计算它们的稳定有理上同调和它们的积分Picard群。利用这些方法，我们给出了亏格至少为9的整Picard群的几何定义的生成元的完整描述，并确定了它们之间的关系。

英文摘要：

We have recently proved a homological stability theorem for moduli spaces of r-Spin Riemann surfaces, which in particular implies a Madsen--Weiss theorem for these moduli spaces. This allows us to effectively study their stable cohomology, and to compute their stable rational cohomology and their integral Picard groups. Using these methods we give a complete description of their integral Picard groups for genus at least 9 in terms of geometrically defined generators, and determine the relations between them.

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