English

The parametric degree of a rational surface

Algebraic Geometry 2007-05-23 v1

Abstract

The parametric degree of a rational surface is the degree of the polynomials in the smallest possible proper parametrization. An example shows that the parametric degree is not a geometric but an arithmetic concept, in the sense that it depends on the choice of the ground field. In this paper, we introduce two geometrical invariants of a rational surface, namely level and keel. These two numbers govern the parametric degree in the sense that there exist linear upper and lower bounds.

Keywords

Cite

@article{arxiv.math/0506097,
  title  = {The parametric degree of a rational surface},
  author = {Josef Schicho},
  journal= {arXiv preprint arXiv:math/0506097},
  year   = {2007}
}

Comments

16 pages, 1 figure

R2 v1 2026-07-22T17:20:20.240Z