What is the state of the art about the kodaira dimension (and rationality, unirationality, etc.) of the moduli spaces of $n$-pointed curves of genus $g$? When it is known and when not? It would be great to collect the references for all $g$ and $n$ but I don't want to look like being fishing for points... :)

Take the 2-minute tour
×

MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.