Normal projective varieties of degree 5

TL;DR

This paper classifies irreducible, reduced, and non-degenerate normal projective varieties of degree five, providing specific results for smooth cases and low dimensions over algebraically closed fields.

Contribution

It offers a comprehensive classification of degree five normal projective varieties, including new results for smooth varieties and surfaces over algebraically closed fields.

Findings

Classification of degree five varieties in projective space

Results for smooth and low-dimensional cases

Explicit descriptions over algebraically closed fields

Abstract

We list the irreducible reduced and not degenerate normal projective varieties $X\subset\mathbb{P}^N$ of dimension $n$ and degree five defined over an algebraically closed field $k$ of char$(k) = 0$. In the smooth case, or when $n = 2$, we give also classification results for any algebraically closed field $k$ of char$(k) \geq 0$.