论文标题
Weierstrass量度的极限在稳定曲线上
Limit of Weierstrass Measure on Stable Curves
论文作者
论文摘要
本文的目的是研究WeierStrass措施在平滑曲线上的限制行为，因为曲线接近一定的淋巴结稳定曲线，该曲线以Deligne-Mumford compactification $ \ bar {\ bar {\ Mathcal m} _g $ $ \ n MATH COLLIE $ \ MATH COUMER的某个点表示，包括Mathcal $ \ Mathercal irred c {m紧凑型类型。结果，在$ \ Mathcal {M} _g $边界处的稳定有理曲线上的WeierStrass测量已完全确定。在此过程中，还研究了伯格曼措施的渐近行为。
The goal of the paper is to study the limiting behavior of the Weierstrass measures on a smooth curve of genus $g\geqslant 2$ as the curve approaches a certain nodal stable curve represented by a point in the Deligne-Mumford compactification $\bar{\mathcal M}_g$ of the moduli $\mathcal{M}_g$, including irreducible ones or those of compact type. As a consequence, the Weierstrass measures on a stable rational curve at the boundary of $\mathcal{M}_g$ are completely determined. In the process, the asymptotic behavior of the Bergman measure is also studied.
