Corpus ID: 16491006

VERTICAL BRAUER GROUPS AND DEL PEZZO SURFACES OF DEGREE 4

@article{VrillyAlvarado2010VERTICALBG,
  title={VERTICAL BRAUER GROUPS AND DEL PEZZO SURFACES OF DEGREE 4},
  author={Anthony V{\'a}rilly-Alvarado and Bianca Viray},
  journal={arXiv: Algebraic Geometry},
  year={2010}
}
We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical, that is, that every Brauer class is obtained by pullback from an element of Brk(P 1 ) for some rational map f : X 99K P 1 . As a consequence, we prove that a Brauer class does not obstruct the existence of a rational point if and only if there exists a ber of f that is locally solvable. The proof is constructive and gives a simple and practical algorithm, distinct from that in (BBFL07), for computing… Expand

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