关于有界域商空间上 Lang 猜想的注记
复变函数
2024-04-17 v3 代数几何
摘要
Lang 猜想：一个复射影流形是 Kobayashi 双曲的，当且仅当它是一般型的且其所有子簇也都是一般型的。我们验证了这一猜想对如下射影流形成立：其万有覆盖带有一个有界的、严格多次调和函数。这特别包含了有界域的紧自由商空间。
引用
@article{arxiv.1809.02398,
title = {A note on Lang's conjecture for quotients of bounded domains},
author = {Sébastien Boucksom and Simone Diverio},
journal= {arXiv preprint arXiv:1809.02398},
year = {2024}
}
备注
10 pages, no figures, comments are welcome. v3: following suggestions made by the referee, the exposition has been improved all along the paper, we added a variant of Theorem A which includes manifolds whose universal cover admits a bounded psh function which is strictly psh just at one point, and we added a section of examples. Final version, to appear on \'Epijournal G\'eom. Alg\'ebrique