On algebraic space filling curves
Algebraic Geometry
2023-10-17 v1
Abstract
Poonen and Gabber independently showed that any smooth geometrically irreducible projective scheme over a finite field has a smooth space filling curve, that is, a smooth curve defined over the field and passes through all points over the field. However, except the case of projective plane, no concrete example was found in literature. In this note, we construct explicit examples of algebraic space filling curves in three dimensional projective space, in particular the ones with minimum degree.
Keywords
Cite
@article{arxiv.2310.09293,
title = {On algebraic space filling curves},
author = {Alana Campbell and Flora Dedvukaj and Donald McCormick and Han-Bom Moon and Joshua Morales},
journal= {arXiv preprint arXiv:2310.09293},
year = {2023}
}
Comments
11 pages, an REU project at Fordham University