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Algebraic and complex geometry

A characteristic-zero counterexample to Lipman–Zariski

OpenAI research collection · 1 manuscript · Source checked 2026-10-19

OpenAI's result summary

Constructs a singular normal affine complex surface with free rank-two tangent sheaf, disproving the characteristic-zero Lipman–Zariski conjecture.

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MANUSCRIPT 01

A singular normal affine surface with free tangent sheaf

We construct a singular normal affine complex surface whose tangent sheaf is free of rank two. This disproves the Lipman–Zariski conjecture in characteristic zero.

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