81 citations · 242 across the 17 of their papers we have counts for
13 papers · 1 filter
Plane Cremona maps preserving a Euclidean volume form
Marc Abboud, Jérémy Blanc, Stéphane Lamy
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…
Tame polynomial automorphisms
Stéphane Lamy
The group of polynomial automorphisms of the affine n-space is an interesting large group. A slightly simpler group is its subgroup of tame automorphisms. Natural problems about th…
Generating the plane Cremona groups by involutions
Stéphane Lamy, Julia Schneider
We prove that over any perfect field the plane Cremona group is generated by involutions.
Quotients of higher dimensional Cremona groups
Jérémy Blanc, Stéphane Lamy, Susanna Zimmermann
We study large groups of birational transformations Bir(X), where X is a variety of dimension at least 3, defined over C or a subfield of C. Two prominent cases are when X is the p…
Signature morphisms from the Cremona group over a non-closed field
Stéphane Lamy, Susanna Zimmermann
We prove that the plane Cremona group over a perfect field with at least one Galois extension of degree 8 is a non-trivial amalgam, and that it admits a surjective morphism to a fr…
On birational maps from cubic threefolds
Jérémy Blanc, Stéphane Lamy
We characterise smooth curves in a smooth cubic threefold whose blow-ups produce a weak-Fano threefold. These are curves of genus and degree , such that (i) $2(d-5) \le…
Automorphisms of open surfaces with irreducible boundary
Adrien Dubouloz, Stéphane Lamy
Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an al…
On the genus of birational maps between 3-folds
Stéphane Lamy
In this note we present two equivalent definitions for the genus of a birational map X --> Y between smooth complex projective 3-folds. The first one is the definition introduced i…
Birational self-maps and piecewise algebraic geometry
Stéphane Lamy, Julien Sebag
Let X be a smooth projective complex variety, of dimension 3, whose Hodge numbers h^{3,0}(X), h^{1,0}(X) both vanish. Let f: X--> X be a birational map that induces an isomorphism…
Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links
Jérémy Blanc, Stéphane Lamy
We characterise smooth curves in P^3 whose blow-up produces a threefold with anticanonical divisor big and nef. These are curves C of degree d and genus g lying on a smooth quartic…
The tame and the wild automorphisms of an affine quadric threefold
Stéphane Lamy, Stéphane Vénéreau
We prove the existence of wild automorphisms on an affine quadric threefold. The method we use is an adaptation of the one used by Shestakov and Umirbaev to prove the existence of…
Normal subgroups in the Cremona group (long version)
Serge Cantat, Stéphane Lamy
Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy make…
Variations on Log Sarkisov Program for Surfaces
Adrien Dubouloz, Stéphane Lamy
Let (S, BS) be the log-pair associated with a compactification of a given smooth quasi-projective surface V . Under the assumption that the boundary BS is irreducible, we propose a…