Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$.
It seems to be important in physics to study the degeneration of certain functions on $\overline{M_g}$ as you approach its boundary.
For which functions on $M_g$ is it interesting to physicists to study their degeneration as you approach the boundary?
I know of theta functions, Green functions and delta invariants. Are there others?
As in my other question, here is an article by Wentworth which I find interesting.
