中文

关于带标记曲线模空间的有理性

代数几何 2007-05-23 v3

摘要

受近期关于带 n 个标记点的亏格 g 稳定曲线模空间 \CalMˉg,n\bar{\Cal M}_{g,n} 几何的若干结果启发,本文通过利用一般曲线的合适平面模型,确定了它们在 g 和 n 取小值时的双有理结构。更确切地说,我们证明了 \CalMg,n{\Cal M}_{g,n}g=2g=21n121\le n\le 12g=3g=31n141\le n\le 14g=4g=41n151\le n\le 15g=5g=51n121\le n\le 12 时是有理的。

关键词

引用

@article{arxiv.math/0504249,
  title  = {On the rationality of moduli spaces of pointed curves},
  author = {Gianfranco Casnati and Claudio Fontanari},
  journal= {arXiv preprint arXiv:math/0504249},
  year   = {2007}
}

备注

Final version accepted for publication on the Journal of the London Mathematical Society (Section 6 of the previous version has been removed since the proof of Claim 6.3 contained a gap)