Del Pezzo surfaces of degree four
B. Eh. Kunyavskij, A. N. Skorobogatov, M. A. Tsfasman (1989)
Mémoires de la Société Mathématique de France
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B. Eh. Kunyavskij, A. N. Skorobogatov, M. A. Tsfasman (1989)
Mémoires de la Société Mathématique de France
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Alexei N. Skorobogatov (1993)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Brendan Hassett, Yuri Tschinkel (2014)
Open Mathematics
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We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.
Andreas-Stephan Elsenhans, Jörg Jahnel (2012)
Open Mathematics
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We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.
Cragnolini, P., Oliverio, P.A. (2000)
Portugaliae Mathematica
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Jurii I. Manin (1966)
Publications Mathématiques de l'IHÉS
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N. I. Shepherd-Barron (1989)
Compositio Mathematica
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Fedor Bogomolov, Viktor Kulikov (2013)
Open Mathematics
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The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙm+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian)] for coverings of projective plane branched in a special class of rational curves. ...
P. C. Craighero, R. Gattazzo (1989)
Rendiconti del Seminario Matematico della Università di Padova
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