Rational Variant of Hartogs' Theorem on Separate Holomorphicity

Author:

Hanwen Liu

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Complex Variables (math.CV)

journal:

date:

2023-07-03 16:00:00

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.

PDF: Rational Variant of Hartogs' Theorem on Separate Holomorphicity.pdf