关于Hain和Looijenga猜想的注记
A remark on a conjecture of Hain and Looijenga
摘要：
在回顾了曲线的模空间的重言式代数及其部分紧化，并陈述了关于这些代数的几个著名结果和定理之后，我们证明了Hain和Looijenga在1996年提出的一个猜想的尖曲线情形的自然扩张为真当且仅当其中两个定理为真.
英文摘要：
After recalling the various tautological algebras of the moduli space of curves and some of its partial compactifications and stating several well-known results and conjectures concerning these algebras, we prove that the natural extension to the case of pointed curves of a 1996 conjecture of Hain and Looijenga is true if and only if two of the stated conjectures are true.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
