论文标题
H-Tautologicy环
The H-tautological ring
论文作者
论文摘要
我们将稳定曲线模量的重言式类别的理论扩展到可允许的曲线覆盖层的模量空间的更一般环境，从而引入了所谓的H-Tautologicy环。主要的新功能是存在限制性限制的形态，记住了Galois覆盖物的中级商，这是新阶级的丰富来源。特别是，我们的新框架包括Harris-Mumford的类别，可允许在模量曲线的空间上封面，在某些曲线中，这些框架在某些示例中是众所周知的，可以在通常的重言式戒指之外。我们为H-Tautologicy环提供了添加剂发电机，并表明它们的相互作用可能是基于Schmitt-Van Zelm的作品来计算的算法。作为一种应用，我们提供了一种计算哈里斯·蒙福德基因座积分的方法，以针对互补维度的重言式类别，恢复并给出了对椭圆曲线封面作者最近的准模块化结果的轻度概括。
We extend the theory of tautological classes on moduli spaces of stable curves to the more general setting of moduli spaces of admissible Galois covers of curves, introducing the so-called H-tautological ring. The main new feature is the existence of restriction-corestriction morphisms remembering intermediate quotients of Galois covers, which are a rich source of new classes. In particular, our new framework includes classes of Harris-Mumford admissible covers on moduli spaces of curves, which are known in some (and speculatively many more) examples to lie outside the usual tautological ring. We give additive generators for the H-tautological ring and show that their intersections may be algorithmically computed, building on work of Schmitt-van Zelm. As an application, we give a method for computing integrals of Harris-Mumford loci against tautological classes of complementary dimension, recovering and giving a mild generalization of a recent quasi-modularity result of the author for covers of elliptic curves.
