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Nonrational Weighted Hypersurfaces

Published online by Cambridge University Press:  11 January 2016

Takuzo Okada
Takuzo Okada*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan, takuzo@kurims.kyoto-u.ac.jp
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Abstract

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The aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].

Keywords

14E0814J4514J3014J70

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 194 , 2009, pp. 1 - 32
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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