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Quotients of groups of birational transformations of cubic Del Pezzo fibrations (1907.04696v2)
Published 10 Jul 2019 in math.AG and math.GR
Abstract: We prove that the group of birational transformations of a Del Pezzo fibration of degree 3 over a curve is not simple, by giving a surjective group homomorphism to a free product of infinitely many groups of order 2. As a consequence we also obtain that the Cremona group of rank 3 is not generated by birational maps preserving a rational fibration. Besides, its subgroup generated by all connected algebraic subgroups is a proper normal subgroup.
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