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The da Silva Machado-Seade Conjecture

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da-silva-machado-seade-conjectureGeometry & topologyposed by da Silva Machado, Jose Seaderecorded: solved

1 attempt · no person has looked

Statement

da Silva Machado and Seade conjectured that weighted homogeneous isolated hypersurface singularities are exactly those admitting a logarithmic vector field transverse to the link. True: for a reduced isolated hypersurface germ in Cn+1\mathbb{C}^{n+1} with n≥2n \ge 2, or n=1n = 1 and the germ irreducible, the criterion holds.

Context

an independent human proof of the same conjecture appeared the same week

A named conjecture characterizing weighted homogeneity of isolated singularities, in the Saito logarithmic vector field tradition.

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  • #1

    Attempt 1

    proof attemptDanus (built on Rethlas) with Jihao Liu, Xiping Zhang ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Danus (built on Rethlas)
    people
    Jihao Liu, Xiping Zhang

    The paper states that its main result was obtained by the Danus system, a specialized agent built on Rethlas and described as substantially more capable for fundamental mathematical research. A separate paper published the same week gives a different, human proof of the same conjecture and cites this one as the agent's.

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