https://arxiv.org/html/2607.22198
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- The Hessian conjecture in dimension 2n implies the Jacobian conjecture in dimension n
Supports. The preprint restates the doubling bridge with a full proof, credited to Meng's 2006 paper, and then exercises it in contrapositive: the six-variable doubling of the three-variable Jacobian counterexample is written out explicitly and shown to have constant Hessian determinant −4 and non-injective gradient. The proof is self-contained and does not depend on the correctness of the counterexample. Sep 15, 2026
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Proposition 2.3. HC_{2n} ⟹ JC_n. Proof (following [6]). Given F: 𝕜^n → 𝕜^n with Jac F ∈ 𝕜^×, set φ(x,y) = ⟨y, F(x)⟩, a polynomial in 𝕜[x_1,…,x_n,y_1,…,y_n].
Supports. The preprint restates the doubling bridge with a full proof, credited to Meng's 2006 paper, and then exercises it in contrapositive: the six-variable doubling of the three-variable Jacobian counterexample is written out explicitly and shown to have constant Hessian determinant −4 and non-injective gradient. The proof is self-contained and does not depend on the correctness of the counterexample.
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- Sep 15, 2026ReadingSteward of “The Hessian conjecture in dimension 2n implies…” · supports, read whole
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