# Sheaf Of regular functions

## TL;DR

This paper proves that for an affine variety V in affine n-space, the structure sheaf O_V is a sheaf of regular functions, establishing (V, O_V) as a locally ringed space, which is fundamental in algebraic geometry.

## Contribution

The paper demonstrates that the structure sheaf on an affine variety is a sheaf of regular functions, confirming the locally ringed space structure.

## Key findings

- O_V is a sheaf of regular functions on V
- (V, O_V) forms a locally ringed space
- Provides foundational result for affine varieties

## Abstract

In this paper, we proved that for an affine variety V in A^n; O_V is a sheaf of regular functions and the ringed space pair (V;O_V ) is a locally ringed space.

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Source: https://tomesphere.com/paper/1901.04137