math.AG — Algebraic Geometry

The fifteenth cohomology of moduli spaces of stable curves

Contributed by zeming sun, guoxiong gao, shurui liu

We determine the fifteenth cohomology of the moduli stack of stable curves $\overline{\mathcal{M}}_{g,n}$ in every genus $g$ and number of markings $n$, with its symmetric-group action, by providing explicit multiplicity formulas for its simple constituents. We also prove the generalized Hodge conjecture in this case. The main result of this paper was obtained using the Pharos system. The author has reviewed the arguments and developed an understanding of the proof. On the basis of this review, the author believes the paper to be correct.