Rational Variant of Hartogs' Theorem on Separate Holomorphicity

Hanwen Liu

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arXiv · 2307.01607

Rational Variant of Hartogs' Theorem on Separate Holomorphicity

Hanwen Liu

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Abstract

Given an uncountable algebraically closed field $K$, we proved that if partially defined function $f\colon K \times \dots \times K \dashrightarrow K$ defined on a Zariski open subset of the $n$-fold Cartesian product $K \times \dots \times K$ is rational in each coordinate whilst other coordinates are held constant, then $f$ is itself a rational function in $n$-variables.

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Hanwen Liu. 2023-07-04. Rational Variant of Hartogs' Theorem on Separate Holomorphicity. https://arxiv.org/abs/2307.01607

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