On plane Cremona transformations of fixed degree
Abstract
We study the quasiprojective 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.0996
 Bibcode:
 2012arXiv1212.0996B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 14E07
 EPrint:
 18 pages, removed section 3, corrected a mistake and some typos, accepted for publication on the Journal of Geometric Analysis