A regular interpolation problem and its applications

TL;DR

This paper proves a new interpolation theorem for regular functions between affine varieties, showing conditions under which a function can be extended globally, and explores its applications in algebraic geometry.

Contribution

It establishes a novel interpolation result linking regular functions and maps between affine varieties under factorial and surjectivity conditions.

Findings

Proves that a regular function composed with a regular map is globally extendable under certain conditions.

Identifies factoriality and almost surjectivity as key conditions for the extension.

Provides applications demonstrating the utility of the interpolation problem in algebraic geometry.

Abstract

In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that coincide with the function on the image of the regular map provided the target variety is factorial and the regular map is almost surjective. We also discuss a few applications of the interpolation problem.