Displaying similar documents to “Dynamics on blowups of the projective plane”

Quartic del Pezzo surfaces over function fields of curves

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.

On the order three Brauer classes for cubic surfaces

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.

On the irreducibility of Hilbert scheme of surfaces of minimal degree

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. ...