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Positivity of Chern Classes of Symmetric Powers

Geometry & topology · posed by classical enumerative geometry · solved

1 comment

Statement

The total Chern class of Symd(Cn)\mathrm{Sym}^d(\mathbb{C}^n) as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Gergely Berczi and Laszlo M. Feher, using AlphaEvolve, ChatGPT 5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The paper calls itself a case study in synchronized AI-assisted mathematics and separates the two roles: AlphaEvolve served first as a searching engine and later as what the authors call a detective for structural recurrences, including a section-long account of one conjecture; ChatGPT 5.5 Pro acted as an interactive assistant for symbolic derivations.

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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.