Stable rationality of orbifold Fano 3-fold hypersurfaces

Okada, Takuzo

doi:10.1090/jag/712

Author: Takuzo Okada
Journal: J. Algebraic Geom. 28 (2019), 99-138
DOI: https://doi.org/10.1090/jag/712
Published electronically: September 26, 2018
MathSciNet review: 3875362
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Abstract | References | Additional Information

Abstract: We determine the rationality of very general quasi-smooth Fano $3$-fold weighted hypersurfaces completely and determine the stable rationality of them except for cubic $3$-folds. More precisely we prove that (i) very general Fano $3$-fold weighted hypersurfaces of index $1$ or $2$ are not stably rational except possibly for the cubic 3-folds, (ii) among the $27$ families of Fano 3-fold weighted hypersurfaces of index greater than $2$, very general members of $7$ specific families are not stably rational, and the remaining $20$ families consist of rational varieties.

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Additional Information

Takuzo Okada
Affiliation: Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan
MR Author ID: 873741
Email: okada@cc.saga-u.ac.jp

Received by editor(s): October 13, 2016
Received by editor(s) in revised form: September 4, 2017, and November 2, 2017
Published electronically: September 26, 2018
Additional Notes: The author would like to thank Professor Ivan Cheltsov for having interest in this work. The author was partially supported by JSPS KAKENHI grant number 26800019.
Article copyright: © Copyright 2018 University Press, Inc.