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On the equations for universal torsors over del Pezzo surfaces

Part of: Surfaces and higher-dimensional varieties Lie groups

Published online by Cambridge University Press:  11 August 2009

Vera V. Serganova  and
Alexei. N. Skorobogatov
Vera V. Serganova
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA (serganov@math.berkeley.edu)
Alexei. N. Skorobogatov
Affiliation:
Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2BZ, UK (a.skorobogatov@imperial.ac.uk) and Institute for Information Transmission Problems, Russian Academy of Sciences, 19 Bolshoi Karetnyi, Moscow 127994, Russia
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Abstract

We describe equations of the universal torsors over del Pezzo surfaces of degrees from 2 to 5 over an algebraically closed field in terms of the equations of the corresponding homogeneous space G/P. We also give a generalization for fields that are not algebraically closed.

Keywords

del Pezzo surfacesuniversal torsorssemisimple Lie groupshomogeneous spaces

MSC classification

Secondary: 14J26: Rational and ruled surfaces 22E46: Semisimple Lie groups and their representations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 1 , January 2010 , pp. 203 - 223
Copyright
Copyright © Cambridge University Press 2010

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