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Advances in Mathematics, 2021, Volume 378, Pages 107541–32 (Mi admat23)  
This article is cited in 10 scientific papers (total in 10 papers)

Birational boundedness of rationally connected Calabi-Yau 3-folds

Weichung Chena, Gabriele Di Cerbob, Jingjun Hanc, Chen Jiangd, Roberto Svaldie

a Graduate School of Mathematical Sciences, the University of Tokyo, Tokyo, Japan
b Department of Mathematics, Princeton University, Princeton, NJ, USA
c Department of Mathematics, Johns Hopkins University, Baltimore, MD, USA
d Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China
e EPFL, Lausanne, Switzerland
Citations (10)
Abstract: We prove that rationally connected Calabi–Yau 3-folds with Kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected 3-folds of $\epsilon$-CY type form a birationally bounded family for $\epsilon>0$. Moreover, we show that the set of $$\epsilon-lc log Calabi–Yau pairs $(X,B)$ with coefficients of $B$ bounded away from zero is log bounded modulo flops. As a consequence, we deduce that rationally connected klt Calabi–Yau 3-folds with mld bounded away from 1 are bounded modulo flops.
Funding agency Grant number
NAKAMURA scholarship
UTokyo System of Support for Graduate Research
National Science Foundation DMS-1702358
Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT)
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) JP16K17558
Churchill College, Cambridge
The authors would like to thank Yoshinori Gongyo for suggesting this topic. WC was supported by NAKAMURA scholarship and the UTokyo System of Support for Graduate Research. WC would like to thank his advisor Yoshinori Gongyo for supporting a visit to the University of Cambridge, where he had valuable discussions with Caucher Birkar and RS. DC was supported in part by NSF Grant DMS-1702358. JH would like to thank his advisors Gang Tian and Chenyang Xu in particular for constant support and encouragement. CJ was supported by JSPS KAKENHI Grant Number JP16K17558 and World Premier International Research Center Initiative (WPI), MEXT, Japan. RS was partially supported by Churchill College, Cambridge. Part of this work was completed during a visit of RS to Princeton University. RS would like to thank Princeton University for its hospitality and the nice working environment, and Janos Kollar for funding his visit. We are grateful to Keiji Oguiso for discussions on examples, and Zhiyu Tian for discussions related to the material in the Appendix. We thank the referees for useful comments.
English version:

DOI: https://doi.org/10.1016/j.aim.2020.107541
Bibliographic databases:
Document Type: Article
Language: English
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