Transcendental obstructions to weak approximation on general K3 surfaces
By Brendan Hassett, Anthony Várilly-Alvarado, P. Varilly. 2010
67 citations recorded by the source corpus.
Abstract We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer–Manin obstruction to weak approximation. To do so, we exploit the relationship between polarized K3 surfaces endowed with particular kinds of Brauer classes and cubic fourfolds.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/78bba0662e39043a43979cc9d4ecfa73a17583b7
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In Applied Mathematics
In Geometry and Topology
- Emanuele Macrì
- P. Stellari
- Franccois Charles
- Brendan Hassett
- D. Huybrechts
- Arend Bayer
- Chunyi Li
- Benjamin Schmidt
Citations in the corpus
- Fano varieties of cubic fourfolds containing a plane (2009, background): “-stable objects in Awith Mukai vector v. Hence, by Theorem 1.3, Mf is isomorphic to Mσm(S,v,B) and so to F(Y). (ii) Questions related to the geometry of the birational models of F(Y) are addressed in [17]. See also [16] for the study of the birational automorphisms of the Fano varieties of lines of ”
- On the Picard number of K3 surfaces over number fields (2011, methodology): “This gives a theoretical explanation to the computations in [van Luijk 2007; Elsenhans and Jahnel 2008a; 2008b; Hassett et al. 2011; Hassett and VárillyAlvarado 2013].”
- Cubic Fourfolds, K3 Surfaces, and Rationality Questions (2016, methodology): “ere η is the class in the Brauer group of S arising from r; note that η = 0 if and only if the three equivalent conditions above hold. Applications of this geometry to rational points may be found in [HVAV11]. Remark 2. The technique of Theorem 1 applies to all smooth projective fourfolds admiting q”