English

Birational geometry of rational quartic surfaces

Algebraic Geometry 2020-07-30 v2

Abstract

Two birational subvarieties of P^n are called Cremona equivalent if there is a Cremona modification of P^n mapping one to the other. If the codimension of the varieties is at least 2 then they are always Cremona Equivalent. For divisors the question is much more subtle and a general answer is unknown. In this paper I study the case of rational quartic surfaces and prove that they are all Cremona equivalent to a plane.

Keywords

Cite

@article{arxiv.1905.03976,
  title  = {Birational geometry of rational quartic surfaces},
  author = {Massimiliano Mella},
  journal= {arXiv preprint arXiv:1905.03976},
  year   = {2020}
}

Comments

Improved exposition after referee comments, 10 pages

R2 v1 2026-06-23T09:02:29.753Z