一些经典不变量，从调和四元组到三角群
Some Classical Invariants, from Harmonic Quadruples to Triangle Groups
AI总结：
本文通过调和四元组与三角群的类比，探讨经典不变量理论及模形式的发展，包含希尔伯特论文的讨论和附录练习。
摘要：
这些笔记是2025年5月在特罗姆瑟举行的“Lie-Stormer暑期学校：从经典到现代的发展中的不变量理论”讲座的扩展版本，属于TiME活动框架内。我们强调二元四次曲线与三元三次曲线（以及随后的模形式）之间的类比，基于它们的调和和等调和不变量。三角群在椭圆和双曲设定中被呈现，附带其相关的镶嵌。主题包括讨论一篇简短的希尔伯特论文，该论文讨论了幂次多项式，该论文被提交给参与者。附录包含一些练习，附有解题草图，以及由文森佐·加拉诺编辑的关于皮法恩（Pfaffians）的专节。
英文摘要：
These notes are an expanded version of the lectures held in Tromso, in May 2025 at the "Lie-Stormer Summer School : Invariant Theory from classics to modern developments", in the framework of TiME events. We emphasize the analogy between binary quartics and ternary cubics (and subsequently modular forms) based on their harmonic and equianharmonic invariants. Triangle groups are presented in both the elliptic and the hyperbolic setting with their associated tilings. The topics include the discussion of a short Hilbert paper on polynomials which are powers, that was proposed to the participants. The appendix contains some exercises, with sketches of solutions, and a section devoted to Pfaffians edited by Vincenzo Galgano.
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。
