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The fifteenth cohomology of moduli spaces of stable curves

Primarily AI-generated textHuman understanding: some partsmath.AG — Algebraic Geometry

Contributed by zeming sun ↗, guoxiong gao, shurui liu

Version 1 / Oct 17, 2026 / CC BY 4.0

Abstract

We determine the fifteenth cohomology of the moduli stack of stable curves M‾g,n\overline{\mathcal{M}}_{g,n} in every genus gg and number of markings nn, 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.

Provenance statement

Pharos carried out the mathematical investigation and drafted the manuscript. The author has reviewed and understood the main mathematical tools and methods used in the calculations, but has not checked all details of the combinatorial classifications and computations.

Tools used

OpenAI
ChatGPTVersion GPT-6 Astra
Pharos team
Pharos

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Version history

  1. v1Submitted by zeming sunRevised after moderator-requested changesCurrentOct 17, 2026