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Bulletin of the London Mathematical Society Advance Access originally published online on November 11, 2008
Bulletin of the London Mathematical Society 2008 40(6):965-971; doi:10.1112/blms/bdn078
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© 2008 London Mathematical Society

Plain varieties

Gábor Bodnár

RISC Software Ges.m.b.H.
Softwarepark 35 (IT-Center)
A-4232 Hagenberg, Austria
Gabor.Bodnar@risc.uni-linz.ac.at

Herwig Hauser

Fakultät für Mathematik
Universität Wien
Nordbergstraße 15
A-1090 Wien, Austria

Josef Schicho

Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Austrian Academy of Sciences
Altenbergerstraße 69
A-4040 Linz, Austria
josef.schicho@oeaw.ac.at

Orlando Villamayor U.

Departamento de Matemáticas
Universidad Autónoma de Madrid
E-28049 Madrid, Spain
villamayor@uam.es

Received 15 May 2007. Revision received 30 May 2008.

Algebraic varieties that are locally isomorphic to open subsets of affine space will be called plain. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and is unknown in general. It is shown that plain varieties are stable under blowup in smooth centers.

2000 Mathematics Subject Classification 14E05, 14M20, 14A10.

The authors have been supported by the Austrian Science Fund (FWF) in the frame of project P18992 [GenBank] and project SFB 1303, and by the Austrian Exchange Service (ÖAD) in the frame of ’Acciones Integradas’.


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