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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.

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Motivations to study the cohomology of the moduli space of curves

Could anyone give some interesting motivations to understand the cohomology of $\mathcal{M}_g$? What I know: I have read the various approaches to construct $\mathcal{M}_g$ via orbit spaces for group …
Taisong Jing's user avatar