Bright, M.J. and Bruin, N. and Flynn, E. V. and Logan, A. (2007) The BrauerManin Obstruction and Sha[2]. LMS Journal of Computation and Mathematics, 10 . pp. 354377. ISSN 14611570

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Official URL: http://www.lms.ac.uk/jcm/
Abstract
We discuss the BrauerManin obstruction on del Pezzo surfaces of degree 4. We outline a detailed algorithm for computing the obstruction and provide associated programs in magma. This is illustrated with the computation of an example with an irreducible cubic factor in the singular locus of the defining pencil of quadrics (in contrast to previous examples, which had at worst quadratic irreducible factors). We exploit the relationship with the TateShafarevich group to give new types of examples of Sha[2], for families of curves of genus 2 of the form y^2 = f(x), where f(x) is a quintic containing an irreducible cubic factor.
Item Type:  Article 

Subjects:  H  N > Number theory 
Research Groups:  Number Theory Group 
ID Code:  797 
Deposited By:  E. Victor Flynn 
Deposited On:  01 Sep 2009 07:35 
Last Modified:  29 May 2015 18:29 
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