Minimal algebraic space filling curves on the product of projective lines

TL;DR

This paper explores the existence and construction of minimal degree smooth algebraic space filling curves on the product of projective lines, providing explicit examples and extending previous results.

Contribution

It introduces new explicit examples of minimal algebraic space filling curves on the product of projective lines, expanding known existence results.

Findings

Numerous explicit examples of such curves are constructed.

The work extends previous existence results by Homma and Kim.

The paper demonstrates the abundance of these curves in the specified setting.

Abstract

We investigate minimal degree smooth algebraic space filling curves on the product of projective lines. We prove that there are plenty of examples in an explicit sense, extending the existence result of Homma and Kim.