Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)

TL;DR

This paper presents efficient algorithms for parametrizing Del Pezzo surfaces of degree 5 over a field k, constructing explicit examples, and determining isomorphism classes, advancing computational methods in algebraic geometry.

Contribution

It introduces new algorithms for parametrizing Del Pezzo surfaces of degree 5, including explicit constructions and isomorphism classification methods.

Findings

Efficient parametrization algorithms for degree 5 Del Pezzo surfaces.

Procedures for constructing explicit examples in each isomorphism class.

Algorithms for deciding equivalence of Del Pezzo surfaces.

Abstract

It is well known that every Del Pezzo surface of degree 5 defined over k is parametrizable over k. In this paper we give an efficient construction for parametrizing, as well as algorithms for constructing examples in every isomorphism class and for deciding equivalence.