OpenAI reports a complex Lipman–Zariski counterexample

There is a singular normal integral affine surface over the complex numbers whose tangent module is free of rank two on the whole surface.

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Understanding the problem

Read the background

There is a singular normal integral affine surface over the complex numbers whose tangent module is free of rank two on the whole surface.

Why it matters

If correct, disproves the characteristic-zero Lipman–Zariski conjecture in the first dimension left by the cited isolated-singularity result.

What counts as progress

Can a singular normal complex surface have a free tangent sheaf?

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