81 citations · 242 across the 17 of their papers we have counts for
19 papers
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…
Tits Alternative for the 3-dimensional tame automorphism group
Stéphane Lamy, Piotr Przytycki
We prove the strong Tits alternative for the 3-dimensional tame automorphism group over a field K of characteristic zero.
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.
Introduction to a small cancellation theorem
Stéphane Lamy, Anne Lonjou
This note is intended as an introduction to two previous works respectively by Dahmani, Guirardel, Osin, and by Cantat, Lamy. We give two proofs of a Small Cancellation Theorem for…
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…
Acylindrical hyperbolicity of the three-dimensional tame automorphism group
Stéphane Lamy, Piotr Przytycki
We prove that the group STame() of special tame automorphisms of the affine 3-space is not simple, over any base field of characteristic zero. Our proof is based on the study…
Combinatorics of the tame automorphism group
Stéphane Lamy
We study the group Tame() of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified and (hopefully) simpli…
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…
The tame automorphism group of an affine quadric threefold acting on a square complex
Cinzia Bisi, Jean-Philippe Furter, Stéphane Lamy
We study the group Tame(SL) of tame automorphisms of a smooth affine 3-dimensional quadric, which we can view as the underlying variety of SL(2,). We construct a sq…
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…
Normal subgroup generated by a plane polynomial automorphism
Jean-Philippe Furter, Stéphane Lamy
We study the normal subgroup <f> generated by a non trivial element f in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On one hand if f has l…
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…