English

On plane Cremona transformations of fixed degree

Algebraic Geometry 2013-08-20 v2 Complex Variables

Abstract

We study the quasi-projective variety Bir_d of plane Cremona transformations defined by three polynomials of fixed degree d and its subvariety Bir_d^o where the three polynomials have no common factor. We compute their dimension and the decomposition in irreducible components. We prove that Bir_d is connected for each d and Bir_d^o is connected when d < 7.

Cite

@article{arxiv.1212.0996,
  title  = {On plane Cremona transformations of fixed degree},
  author = {Cinzia Bisi and Alberto Calabri and Massimiliano Mella},
  journal= {arXiv preprint arXiv:1212.0996},
  year   = {2013}
}

Comments

18 pages, removed section 3, corrected a mistake and some typos, accepted for publication on the Journal of Geometric Analysis

R2 v1 2026-06-21T22:49:02.447Z