@article{f876e03ee21147fc8c6fa0324db620f9,
title = "Birational boundedness of rationally connected Calabi–Yau 3-folds",
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 ϵ-CY type form a birationally bounded family for ϵ>0. Moreover, we show that the set of ϵ-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.",
keywords = "Boundedness, Calabi–Yau 3-folds, Rationally connected",
author = "Weichung Chen and {Di Cerbo}, Gabriele and Jingjun Han and Chen Jiang and Roberto Svaldi",
note = "Funding Information: Acknowledgments. 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 J{\'a}nos Koll{\'a}r 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. Funding Information: Acknowledgments . 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 J{\'a}nos Koll{\'a}r 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. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2021",
month = feb,
day = "12",
doi = "10.1016/j.aim.2020.107541",
language = "English (US)",
volume = "378",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}