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The Brauer-Manin obstruction on Del Pezzo surfaces of degree 2

Author:
Corn, Patrick  


Journal:
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY


Issue Date:
2007


Abstract(summary):

This paper explores the computation of the Brauer-Manin obstruction on Del Pezzo surfaces of degree 2, with examples coming from the class of 'semi-diagonal' Del Pezzo surfaces of degree 2. It is conjectured that the failure of the Hasse principle for a broad class of varieties, including Del Pezzo surfaces, can always be explained by a non-trivial Brauer-Manin obstruction. We provide computational evidence in support of this conjecture for semi-diagonal Del Pezzo surfaces of degree 2. In addition, we determine the complete list of the possibilities for the finite abelian group H-1(k, Pic (X) over bar), where X is a Del Pezzo surface of any degree, thus completing a computation which had been previously carried out in various special cases only.


Page:
735---777


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