Commensurating actions of birational groups and groups of pseudo-automorphisms
Copyright policy )Commensurating actions of birational groups and groups of pseudo-automorphisms
Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1 . We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on cat ( 0 ) cubical complexes, for example a discrete group with Kazhdan Property (T), is birationally conjugate to a group acting by pseudo-automorphisms on some non-empty Zariski-open subset. We apply this argument to classify groups of birational transformations of surfaces with this fixed point property up to birational conjugacy.
- University of Rennes 1 France
- Jean Monnet University France
- UNIVERSITE JEAN MONNET SAINT-ETIENNE France
- University of Rennes 2 France
- French National Centre for Scientific Research France
14J50, Group Theory (math.GR), Cremona group, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], 510, Birational automorphisms, Cremona group and generalizations, Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, birational group, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], FOS: Mathematics, 14E07, 20F65, commensurating action, Algebraic Geometry (math.AG), [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT], [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Geometric Topology (math.GT), 14E07 (Primary), 14J50, 20F65 (Secondary), regularization, Automorphisms of surfaces and higher-dimensional varieties, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], algebraic surfaces, Geometric group theory, Mathematics - Group Theory
14J50, Group Theory (math.GR), Cremona group, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], 510, Birational automorphisms, Cremona group and generalizations, Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, birational group, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], FOS: Mathematics, 14E07, 20F65, commensurating action, Algebraic Geometry (math.AG), [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT], [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Geometric Topology (math.GT), 14E07 (Primary), 14J50, 20F65 (Secondary), regularization, Automorphisms of surfaces and higher-dimensional varieties, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], algebraic surfaces, Geometric group theory, Mathematics - Group Theory
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