On plane Cremona transformations of fixed degree

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.

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