2019
DOI: 10.1007/978-3-030-31106-3_17
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Potentially Stably Rational Del Pezzo Surfaces over Nonclosed Fields

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Cited by 5 publications
(2 citation statements)
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“…Quadric threefolds: We consider first X ⊂ P 4 given by 5 j=1 x 2 j = 0, with a natural action of the Weyl group W (D 5 ). This group has 197 conjugacy classes of subgroups, examined in [23,Section 5] in connection with the analysis of possible Galois actions (or automorphisms) on Picard groups of Del Pezzo surfaces of degree 4; the goal there was to identify potentially rational surfaces over nonclosed fields (see also [31]). There are 112 (conjugacy classes of) subgroups G ⊂ W (D 5 ) which give rise to fixed-point free actions.…”
Section: Automorphisms Of Quadricsmentioning
confidence: 99%
“…Quadric threefolds: We consider first X ⊂ P 4 given by 5 j=1 x 2 j = 0, with a natural action of the Weyl group W (D 5 ). This group has 197 conjugacy classes of subgroups, examined in [23,Section 5] in connection with the analysis of possible Galois actions (or automorphisms) on Picard groups of Del Pezzo surfaces of degree 4; the goal there was to identify potentially rational surfaces over nonclosed fields (see also [31]). There are 112 (conjugacy classes of) subgroups G ⊂ W (D 5 ) which give rise to fixed-point free actions.…”
Section: Automorphisms Of Quadricsmentioning
confidence: 99%
“…Such actions have been classified for degree 4 del Pezzo surfaces in [19, p. 15] and for degrees 3, 2, and 1 in [31]. When the surface admits a conic bundle structure W → P 1 over k then the Galois action can be described as follows:…”
Section: Recollections On Stably Rational Non-rational Surfacesmentioning
confidence: 99%