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ON THE ANTI-CANONICAL GEOMETRY OF WEAK $\mathbb {Q}$-FANO THREEFOLDS, III

Part of: Cycles and subschemes Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  22 August 2023

CHEN JIANG Open the ORCID record for CHEN JIANG [Opens in a new window]  and
YU ZOU Open the ORCID record for YU ZOU [Opens in a new window]
CHEN JIANG
Affiliation:
Shanghai Center for Mathematical Sciences and School of Mathematical Sciences Fudan University Shanghai 200438 China chenjiang@fudan.edu.cn
YU ZOU*
Affiliation:
Yau Mathematical Sciences Center Tsinghua University Beijing 100084 China
*
fishlinazy@tsinghua.edu.cn
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Abstract

For a terminal weak ${\mathbb {Q}}$-Fano threefold X, we show that the mth anti-canonical map defined by $|-mK_X|$ is birational for all $m\geq 59$.

MSC classification

Primary: 14J45: Fano varieties
Secondary: 14J30: $3$-folds 14C20: Divisors, linear systems, invertible sheaves 14E05: Rational and birational maps
Type
Article
Information
Nagoya Mathematical Journal , Volume 253 , March 2024 , pp. 23 - 47
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

Jiang was supported by the National Natural Science Foundation of China for Innovative Research Groups (Grant No. 12121001) and the National Key Research and Development Program of China (Grant No. 2020YFA0713200). Jiang is a member of LMNS, Fudan University.

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