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3 results

K-STABLE DIVISORS IN $\mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^2$ OF DEGREE $(1,1,2)$
Part of
- Surfaces and higher-dimensional varieties
- Complex manifolds
IVAN CHELTSOV, KENTO FUJITA, TAKASHI KISHIMOTO, TAKUZO OKADA
Journal: Nagoya Mathematical Journal / Volume 251 / September 2023
Published online by Cambridge University Press: 28 April 2023, pp. 686-714
Print publication: September 2023
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We prove that every smooth divisor in $\mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^2$ of degree $(1,1,2)$ is K-stable.

Stable Rationality of Cyclic Covers of Projective Spaces
Part of
Takuzo Okada
Journal: Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019
Published online by Cambridge University Press: 11 January 2019, pp. 667-682
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The main aim of this paper is to show that a cyclic cover of ℙn branched along a very general divisor of degree d is not stably rational, provided that n ≥ 3 and d ≥ n + 1. This generalizes the result of Colliot-Thélène and Pirutka. Generalizations for cyclic covers over complete intersections and applications to suitable Fano manifolds are also discussed.

Nonrational Weighted Hypersurfaces
Takuzo Okada
Journal: Nagoya Mathematical Journal / Volume 194 / 2009
Published online by Cambridge University Press: 11 January 2016, pp. 1-32
Print publication: 2009
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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].