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AN EFFECTIVE UPPER BOUND FOR ANTI-CANONICAL VOLUMES OF SINGULAR FANO THREEFOLDS

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  07 March 2024

Chen Jiang  and
Yu Zou Open the ORCID record for Yu Zou [Opens in a new window]
Chen Jiang
Affiliation:
Shanghai Center for Mathematical Sciences & School of Mathematical Sciences, Fudan University, Shanghai, 200438, China ([email protected])
Yu Zou*
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China
*
[email protected]
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Abstract

For a real number $0<\epsilon <1/3$, we show that the anti-canonical volume of an $\epsilon $-klt Fano $3$-fold is at most $3,200/\epsilon ^4$, and the order $O(1/\epsilon ^4)$ is sharp.

Keywords

Fano threefoldsanti-canonical volumeslog canonical thresholdsboundedness

MSC classification

Primary: 14J45: Fano varieties
Secondary: 14J30: $3$-folds 14J17: Singularities
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 6 , November 2024 , pp. 2631 - 2646
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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