PreprintCC BY-NC-ND 4.0arXiv
Plane Cremona maps preserving a Euclidean volume form
Abstract
We give a presentation by generators and relations of the group of birational transformations of the plane preserving a differential form with poles along a triple line. This group strictly contains the automorphism group of the affine plane.
Related
- On the quadratic length of plane Cremona maps of degree 4
- On plane Cremona maps of degree 4 and length 2
- p-elementary non-cyclic subgroups of the Cremona group of the plane
- Geodesic nets on the Euclidean plane and closed geodesic nets on Euclidean surfaces
- Singularities of the Wigner Caustic and the Centre Symmetry Set of Frontal Curves in the Euclidean Plane
BibTeX
@misc{abboud2026plane,
title = {{Plane Cremona maps preserving a Euclidean volume form}},
author = {Marc Abboud and Jérémy Blanc and Stéphane Lamy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17432},
eprint = {2610.17432},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17432},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Plane Cremona maps preserving a Euclidean volume form
AU - Marc Abboud
AU - Jérémy Blanc
AU - Stéphane Lamy
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17432
UR - https://arxiv.org/abs/2610.17432
AB - We give a presentation by generators and relations of the group of birational transformations of the plane preserving a differential form with poles along a triple line. This group strictly contains the automorphism group of the affine plane.
ER -