First of all, let me thank you for this amazing serie, it is very well written and pleasant to read.

I am a physicist and I got interested in the study of the moduli space of curves of genus zero because of its connections with quantum field theory.

In particular, I know that the moduli space has certain “factorization properties”, that is in order to compactify it you have to add codimension one strata which are written as products of other moduli spaces : $\partial M_{0,n} \superset M_{0,k} \times M_{0,n-k+2}$

Do you think it would be possible to find a meromorphic form $\omega_n$ of maximum rank such that its divisor is made of exactly these strata and its residue at $M_{0,k} \times M_{0,n-k+2}$ is written as $\omega_k \wedge \omega_{n-k+2}$?

I apologize if the question is ill-posed and lacks of rigour…I am just an humble physicist…

Thank you,

Giulio

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Thanks! ]]>

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