# What is the importance of studying degeneration on $M_g$

+ 5 like - 0 dislike
8 views

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.

This post has been migrated from (A51.SE)
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar\varnothing$sicsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.