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Automorphisms of pointless surfaces
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For a geometrically rational surface X over an arbitrary field of characteristic different from 2 and 3 that contains all roots of 1, we show that either X is birational to a product of a projective line and a conic, or the group of birational automorphisms of X has bounded finite subgroups. As a key step in the proof, we show boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide applications to Jordan property for groups of birational automorphisms.
Forward citations
Cited by 2 Pith papers
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Birational Geometry of sextic del Pezzo surfaces
Degree 6 del Pezzo surfaces over perfect fields are classified biregularly and birationally, and are shown to be the only solid surfaces admitting infinite pliability, with explicit presentations for their birational ...
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Composition of Sarkisov links between del Pezzo surfaces
Over any perfect field, two birationally equivalent del Pezzo surfaces of Picard rank one are connected by a birational map that factors into at most two Sarkisov links, and this bound is optimal.
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