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math.AG2026
On the Hessian Conjecture in Lorentzian Signature: Constant Pivots and Hesse Systems
Hanwen Liu
As a close relative of the Jacobian conjecture, the Hessian conjecture in dimension states that the local Legendre transform of a polynomial solution to the Monge--Ampère equat…
math.AG2023
Rational Variant of Hartogs' Theorem on Separate Holomorphicity
Hanwen Liu
Given an uncountable algebraically closed field , we proved that if partially defined function defined on a Zariski open subs…