On a question of Zariski on Zariski surfaces

We give a new method to construct unirational surfaces which may be applied to the following question posed by Zariski in his studies on unirational surfaces. Is any Zariski surface with geometric genus zero rational? Our main result is a negative answer to this question in any characteristic case.

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 276; no. 1-2; pp. 237 - 242
Main Author Mitsui, Kentaro
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2014
Subjects
Mathematics
Mathematics and Statistics
14G17
Zariski surfaces
Elliptic surfaces
Multiple fibers
Unirational surfaces
14J27
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Summary:We give a new method to construct unirational surfaces which may be applied to the following question posed by Zariski in his studies on unirational surfaces. Is any Zariski surface with geometric genus zero rational? Our main result is a negative answer to this question in any characteristic case.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-013-1195-0