# Algebraic Subset of n-dimensional Vector Space on Affine Scheme

### Jiaming Luo

#### 2023

#### Abstract

In this paper, we study the connection between the most basic Hodge theory in compact complex manifold and the affine scheme in algebraic geometry. By introducing the definitions of algebraic subset and affine scheme, the Hodge operator on -dimensional affine space is defined, the ringed space of algebraic subset defined on affine space is constructed, and the proof the Nullstellensatz theorem is obtained.

Download#### Paper Citation

#### in Harvard Style

Luo J. (2023). **Algebraic Subset of n-dimensional Vector Space on Affine Scheme**. In *Proceedings of the 2nd International Seminar on Artificial Intelligence, Networking and Information Technology - Volume 1: ANIT*; ISBN 978-989-758-677-4, SciTePress, pages 538-541. DOI: 10.5220/0012287200003807

#### in Bibtex Style

@conference{anit23,

author={Jiaming Luo},

title={Algebraic Subset of n-dimensional Vector Space on Affine Scheme},

booktitle={Proceedings of the 2nd International Seminar on Artificial Intelligence, Networking and Information Technology - Volume 1: ANIT},

year={2023},

pages={538-541},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012287200003807},

isbn={978-989-758-677-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Seminar on Artificial Intelligence, Networking and Information Technology - Volume 1: ANIT

TI - Algebraic Subset of n-dimensional Vector Space on Affine Scheme

SN - 978-989-758-677-4

AU - Luo J.

PY - 2023

SP - 538

EP - 541

DO - 10.5220/0012287200003807

PB - SciTePress