# On polynomial extension property in n-disc

## TL;DR

This paper proves that one-dimensional algebraic subsets of the polydisc with the polynomial extension property are holomorphic retracts, extending understanding of polynomial extension in complex analysis.

## Contribution

It establishes that such algebraic subsets with the polynomial extension property are necessarily holomorphic retracts, providing a new characterization in several complex variables.

## Key findings

- One-dimensional algebraic subsets with polynomial extension property are holomorphic retracts.
- The result applies to arbitrarily dimensional polidisc subsets.
- It advances the understanding of polynomial extension properties in complex analysis.

## Abstract

In this note we show that an one-dimensional algebraic subset $\mathcal{V}$ of arbitrarily dimensional polidisc $\mathbb{D}^n$, which has the polynomial extension property, is a holomorphic retract.