强极大秩猜想与曲线模空间
代数几何
2024-09-18 v3
摘要
基于作者近期的工作，我们利用向椭圆曲线链退化证明了Aprodu-Farkas强极大秩猜想在亏格 和 中的两个情形。这构成了Farkas证明亏格22和23曲线模空间为一般型这一纲领中的重大进展。我们的技术结合了Eisenbud-Harris极限线性序列理论，以及第二作者发展的关联线性序列概念。
引用
@article{arxiv.1808.01290,
title = {The strong maximal rank conjecture and moduli spaces of curves},
author = {Fu Liu and Brian Osserman and Montserrat Teixidor i Bigas and Naizhen Zhang},
journal= {arXiv preprint arXiv:1808.01290},
year = {2024}
}
备注
59 pages. v3: Farkas has informed us that his divisor class computation does not suffice to reduce the moduli spaces being of general type to the corresponding cases of the strong maximal rank conjecture: a second type of excess degeneracy also has to be ruled out. We have accordingly removed the implications on the moduli spaces pending further study of the second form of degeneracy