Abstract
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 $\overline{\mathcal{M}}_g$ 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.
Funding Statement
The second-named author was partially supported by a grant from the National Science Foundation.
Citation
Ngai-Fung Ng. Sai-Kee Yeung. "Limit of Weierstrass measure on stable curves." J. Differential Geom. 122 (1) 131 - 153, September 2022. https://doi.org/10.4310/jdg/1668186789
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