预稳定曲线栈的Chow环 II
代数几何
2021-07-21 v1
摘要
我们继续研究在[arXiv:2012.09887v2]中开始的预稳定曲线模栈的Chow环。在亏格时，我们证明的Chow环与 tautological ring 重合，并依据（加法）生成元与关系给出完整描述。这推广了Keel以及Kontsevich-Manin关于稳定曲线空间的早期结果。我们的论证利用模栈的边界分层以及对各层的第一高阶Chow群的研究，特别地给出了Kontsevich和Manin结果的一个新证明。
引用
@article{arxiv.2107.09192,
title = {Chow rings of stacks of prestable curves II},
author = {Younghan Bae and Johannes Schmitt},
journal= {arXiv preprint arXiv:2107.09192},
year = {2021}
}
备注
This paper is the second part of the previous paper [arXiv:2012.09887v1] which has been split off due to length; for the first part [arXiv:2012.09887v2], an appendix (joint with J. Skowera) about proper pushforwards for Chow groups of Artin stacks has been added. 68 pages. Comments are very welcome!